Show, don't tell - but what does that actually mean?

Writers who escape from the malign and clammy fingers of the English teacher and take to fiction are always being told that the way to connect with a reader is to 'Show, don't tell'. But what does it actually mean? If you say, for instance:

It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to Heaven, we were all going direct the other way – in short, the period was so far like the present period, that some of its noisiest authorities insisted on its being received, for good or for evil, in the superlative degree of comparison only.

is this showing or telling? I'll tell you what it is: it's telling. Because the reader is being given a nice big slab of information; you, the writer, are gracing that reader with your opinion and your viewpoint, and nothing's actually happening.
On the other hand, this –

He lay flat on the brown, pine-needled floor of the forest, his chin on his folded arms, and high overhead the wind blew in the tops of the pine trees. The mountainside sloped gently where he lay; but below it was steep and he could see the dark of the oiled road winding through the pass. There was a stream alongside the road and far down the pass he saw a mill beside the stream and the falling water of the dam, white in the summer sunlight.“Is that the mill?” he asked.“Yes.”“I do not remember it.” 

- is showing. But why?
This is why: in the first piece, the beginning of Charles  Dickens' stunning pageturner about the French Revolution, A Tale of Two Cities, Dickens is setting out the mise-en-scène, he's setting up the action first by telling the reader what to think.
In the second piece, Ernest Hemingway's filmic For Whom the Bell Tolls, we jump straight into the action. We have a hero – for Hemingway's characters are always heroes – and a wise old man – for if they're not heroes then they're archetypes – planning to blow up a bridge.
Not that Hemingway's averse to giving you his opinions, but he slithers them into your back pocket under the pretext of telling you what sort of explosives to use, or how thirsty his characters are, or – well, here he is describing his hero:

The young man, who was tall and thin, with sun-streaked fair hair, and a wind- and sun-burned face, who wore the sun-faded flannel shirt, a pair of peasant’s trousers and rope-soled shoes, leaned over, put his arm through one of the leather pack straps and swung the heavy pack up onto his shoulders. He worked his arm through the other strap and settled the weight of the pack against his back. His shirt was still wet from where the pack had rested.“I have it up now,” he said. “How do we go?”“We climb,” Anselmo said.

Very sneaky. But very effective. Not that it's the only only way to write. But it's the only way to write when you're starting to write fiction, because Show, Don't Tell is the magic spell that will free you from the cruel enchantment of those evil English teachers.
When you start to write, you're almost always delighted with all the gorgeous words. Wow! You can use words like 'evanescent'! And 'recursive'!
But you'll go badly wrong if you let the words get you into their net. Because the purpose of writing fiction isn't to show that you've eaten a dictionary. The purpose of writing is to change your reader, by causing an emotional reaction in him, by moving him, by making him see things as you do.
And to do this, you have to get him breathing in synch with you. You have to get the reader feeling that he's experiencing the action.
The best way to do this is to write in action, in scenes. You can give the reader information, but do it in a way that makes the reader control it. I don't know if you remember a film from the 1980s called Diva, about a Vietnamese courier in love with an opera singer who's visiting Paris? In the middle of an intensely complicated and arty and très très French series of twists and turns, the villains corner one of our heroes in a friend's warehouse, where he's hiding out.
We've met this friend, Gorodish, before – when we first meet him, he's chopping onions, wearing a snorkel and a mask to protect himself against the tear-inducing fumes. Later, as one of these same villains is smirkingly about to kill someone, Gorodish appears from behind him, cracks an ampoule of something magical, and the villain's eyes turn up and he folds up into unconsciousness.
Now, Gorodish reappears in the dark, and quietly swings the switch that controls the lights so that it's over the un-railed-off hole where the industrial lift comes up and down. The switch has a red bulb lighting it up so you can see it in the dark.
Teeth gleaming in anticipation, the villain reaches over for the switch, and "Aaaaaaaarrrrgggghhhhhh!!" disappears, and there's a crash below.
Now, that's good writing.
What do you remember from the books you love most? Almost invariably, it's a scene. You may love it for what it portends, like this scene from Pádraic Colum's The King of Ireland's Son –

"Prince," said the old fellow looking up at him, "if you can play a game as well as you can sing a song, I'd like if you would sit down beside me.""I can play any game," said the King of Ireland's Son. He fastened his horse to the branch of a tree and sat down on the heap of stones beside the old man."What shall we play for?" said the gray old fellow."Whatever you like," said the King of Ireland's Son."If I win you must give me anything I ask, and if you win I shall give you anything you ask. Will you agree to that?""If it is agreeable to you it is agreeable to me," said the King of Ireland's Son.

- when you immediately know that this easygoing young lad, who'll go a bit of the road with anyone, is about to get himself into more trouble than he can easily get out of.
Foreshadowing like this is a lovely compliment to the reader: the writer gives the reader a bit of information that's going to come in handy, and the reader is delighted to guess what's likely to happen.
Colum could, of course, have simply told the reader:

"Now, little did the King of Ireland's Son know it, but the man who was asking to play a game of chess with him was a dangerous enchanter"

– and a less skilled writer would have done so. That would be telling.
Instead, he chose to show the unfortunate young lad as his inattention and sloppy good nature topples him from the indulged life of a spoilt boy into all the difficulties and sorrows of an adventurer. And because he showed it, the reader followed eagerly after.
What's your favourite book? What do you remember from it? You may, for instance, remember Jane Austen's famous first line from the comic romance Pride and Prejudice –

It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife.

- but you only remember this nice piece of cattiness because of the action that starts almost immediately -

"My dear Mr Bennet,'' said his lady to him one day, "have you heard that Netherfield Park is let at last?''Mr Bennet replied that he had not."But it is,'' returned she; "for Mrs Long has just been here, and she told me all about it.''Mr Bennet made no answer."Do not you want to know who has taken it?'' cried his wife impatiently."You want to tell me, and I have no objection to hearing it.''This was invitation enough.

And what you remember from the story that follows, with all its satisfying misunderstandings and star-crossings, is almost certainly not Austen's superb prose, the epitome of a well-informed maiden aunt's murmurings, but the action: Mrs Bennet's efforts to get her daughters married to wealthy Mr Bingley and other good prospects; sensible, ethical Elizabeth's dislike of high-nosed Mr Darcy, the schemings of the seducer Wickham, and Elizabeth's turnaround when she discovers that Mr Darcy has secretly paid Wickham's debts so that he can marry… well, you know.
What do you remember of A Tale of Two Cities? Certainly most of the rest is lost to you, while that scene where the worthless Sidney Carton changes place with his heroic lookalike Charles Darney and steps onto the platform of the guillotine with the words "It is a far, far better thing I do than I have ever done…" to save his life and give him to the woman Carton loves.
What do you remember of The Call of the Wild? Every word of Jack London's book is action – and you'll remember the scenes where the dog Buck is rescued after long episodes of brutality, when Buck saves his rescuer from a river, and the end, where Buck, now free, returns to mourn his master.
Romeo and Juliet? There's plenty of resonant language, which you remember because it's woven in with the emotions: if you're asked to recall any scene, it'll be the balcony scene and the death of the two lovers through misunderstandings.
Every good writer does this: brings the story into the consciousness of the reader. Look at Chekhov starting a story:

It was said that a new person had appeared on the sea-front: a lady with a little dog. Dmitri Dmitritch Gurov, who had by then been a fortnight at Yalta, and so was fairly at home there, had begun to take an interest in new arrivals. Sitting in Verney's pavilion, he saw, walking on the sea-front, a fair-haired young lady of medium height, wearing a béret; a white Pomeranian dog was running behind her.And afterwards he met her in the public gardens and in the square several times a day. She was walking alone, always wearing the same béret, and always with the same white dog; no one knew who she was, and every one called her simply "the lady with the dog.""If she is here alone without a husband or friends, it wouldn't be amiss to make her acquaintance," Gurov reflected.

You know immediately what kind of person Gurov is, from just this short passage. Even when Chekhov goes on to give you some information about the character – 

He was under forty, but he had a daughter already twelve years old, and two sons at school. He had been married young, when he was a student in his second year, and by now his wife seemed half as old again as he. She was a tall, erect woman with dark eyebrows, staid and dignified, and, as she said of herself, intellectual. She read a great deal, used phonetic spelling, called her husband, not Dmitri, but Dimitri, and he secretly considered her unintelligent, narrow, inelegant, was afraid of her, and did not like to be at home. He had begun being unfaithful to her long ago -- had been unfaithful to her often, and, probably on that account, almost always spoke ill of women, and when they were talked about in his presence, used to call them "the lower race."

- he does it in such a way that it's causing you, the reader, to form your own opinions, slyly making you feel a sharp dislike of Mr Gurov.
Even in Tipperary man Laurence Sterne's hilarious 18th-century romp through France, A Sentimental Journey -

They order, said I, this matter better in France. - You have been in France? said my gentleman, turning quick upon me, with the most civil triumph in the world. - Strange! quoth I, debating the matter with myself, That one and twenty miles sailing, for ’tis absolutely no further from Dover to Calais, should give a man these rights: - I’ll look into them: so, giving up the argument, - I went straight to my lodgings, put up half a dozen shirts and a black pair of silk breeches, - “the coat I have on,” said I, looking at the sleeve, “will do;” - took a place in the Dover stage; and the packet sailing at nine the next morning, - by three I had got sat down to my dinner upon a fricaseed chicken, so incontestably in France, that had I died that night of an indigestion, the whole world could not have suspended the effects of the droits d’aubaine; - my shirts, and black pair of silk breeches, - portmanteau and all, must have gone to the King of France; - even the little picture which I have so long worn, and so often have told thee, Eliza, I would carry with me into my grave, would have been torn from my neck! - Ungenerous! to seize upon the wreck of an unwary passenger, whom your subjects had beckoned to their coast! - By heaven!  Sire, it is not well done; and much does it grieve me, ’tis the monarch of a people so civilized and courteous, and so renowned for sentiment and fine feelings, that I have to reason with! -

while Sterne is chattering like the chattiest friend you've ever had, you're getting lots of info from the music of what's happening, from what you're being shown, not told.

Violent prologues

The Reader by Derek Kinzett

Fashionable thrillers of the 2000s have an editor-driven trope: the violent prologue, involving someone dying horribly, killed by an unseen villain or a villain who appears only peripherally as a figure of evil in the rest of the book. I find it a pain in the ass, frankly.
It seems to have been brought into the mainstream by the Scandinavians. You know the kind of thing -

Nothing for two thousand miles but snow. The only light: a blood-red seeping of lamplight from the windows of a wooden hovel. If someone is screaming, no one is around to hear.
If you could go inside, you would see a child, strapped to a bed stolen last year from the Ásgeir Haraldssen Hospital for Unfortunate Mites. She is unconscious, yet one wrist still strains at the bindings made from antique Rolex straps. Blood falls slowly and sinks into the ice. Below, somewhere deep below, the ice fish sense the scent of cooling human corpuscles…

Editors love this kind of thing. "That's it, bring the reader into the story with a bang," they say, rubbing their hands. "A good strong opening. Involve the reader. Get the heart pumping."
Yet some of the most wonderful book openings in the world, that drag the reader in by the hair of the head and make it impossible to put the book down, have no violence at all. Looky:

It was a bright cold day in April, and the clocks were striking thirteen. Winston Smith, his chin nuzzled into his breast in an effort to escape the vile wind, slipped quickly through the glass doors of Victory Mansions, though not quickly enough to prevent a swirl of gritty dust from entering along with him.
The hallway smelt of boiled cabbage and old rag mats. At one end of it a coloured poster, too large for indoor display, had been tacked to the wall. It depicted simply an enormous face, more than a metre wide: the face of a man of about forty-five, with a heavy black moustache and ruggedly handsome features. Winston made for the stairs. It was no use trying the lift. Even at the best of times it was seldom working, and at present the electric current was cut off during daylight hours. It was part of the economy drive in preparation for Hate Week. The flat was seven flights up, and Winston, who was thirty-nine and had a varicose ulcer above his right ankle, went slowly, resting several times on the way. On each landing, opposite the lift-shaft, the poster with the enormous face gazed from the wall. It was one of those pictures which are so contrived that the eyes follow you about when you move. BIG BROTHER IS WATCHING YOU, the caption beneath it ran. (George Orwell: 1984)

Or the opening of The Man in the High Castle, Philip K Dick's dystopian multiple-parallel-futures novel, set (mainly) in the Japanese-run San Francisco of a world in which Japan has conquered and occupied the United States in World War II:

For a week Mr. R. Childan had been anxiously watching the mail. But the valuable shipment from the Rocky Mountain States had not arrived. As he opened up his store on Friday morning and saw only letters on the floor by the mail slot he thought, I'm going to have an angry customer.
Pouring himself a cup of instant tea from the five-cent wall dispenser he got a broom and began to sweep; soon he had the front of American Artistic Handcrafts Inc. ready for the day, all spick and span with the cash register full of change, a fresh vase of marigolds, and the radio playing background music. Outdoors along the sidewalk businessmen hurried toward their offices along Montgomery Street. Far off, a cable car passed; Childan halted to watch it with pleasure. Women in their long colorful silk dresses . . . he watched them, too. Then the phone rang. He turned to answer it.
"Yes," a familiar voice said to his answer. Childan's heart sank. "This is Mr. Tagomi. Did my Civil War recruiting poster arrive yet, sir? Please recall; you promised it sometime last week." The fussy, brisk voice, barely polite, barely keeping the code. "Did I not give you a deposit, sir, Mr. Childan, with that stipulation? This is to be a gift, you see. I explained that. A client."
"Extensive inquiries," Childan began, "which I've had made at my own expense, Mr. Tagomi, sir, regarding the promised parcel, which you realize originates outside of this region and is therefore-"

Or what about the opening of Marian Keyes' first book, Rachel's Holiday?

They said I was a drug addict. I found that hard to come to terms with. I was a middle-class, convent-educated girl whose drug use was strictly recreational. And surely drug addicts were thinner?

You want to write an opening that your reader can't put down? Bring the reader straight into your protagonist's life. Slap the protagonist with the central problem of his or her story. Now you've got your reader. Keep talking.