Other people have already said more or less
what I would, but I did want to pop in and point out that this:
Azurne said:
A knight chops off the head of a dragon.
Here, I am telling you a knight chopped off the head of a dragon. There's no more detail about it, there's nothing else to it, really. If I were to show you what happened, it would bear some resemblance to this:
The knight quickly side-stepped to his right and dodged the flaming pillar of fire, wincing from the sheer amount of heat engulfing the spot where he had just stood. Seizing opportunity, he snapped his wrist and brought his long sword up to meet the dragon's neck, making a clean thorough cut and beheading the raging beast.
is not an example of going from telling to showing. The difference between showing and telling isn't whether or not you "show" what happened; it's talking about implying something rather than stating it explicitly. In your second example, after removing all extraneous words, you still have "he beheaded the dragon." You state it explicitly. If you had wanted to "show" that being the case, you could instead do something like, "'Is it over?' Fen asked, peeking out from behind the boulder. 'I suppose you could say that,' Galen replied, tossing the head at the elf's feet and smirking as Fen flinched away." There's no way to transform this to "the knight chops off the head of the dragon," and yet you get a pretty good idea of what went down nonetheless.
The weird thing about "show, don't tell," and the reason I think it confuses people a lot, is that what it's really about is
allowing the reader to draw their own conclusions. It doesn't necessarily involve more words than telling something. And there isn't really any such thing as "showing" in writing to begin with--there's only
telling different things. Azurne's first example, of the sad girl,
is an example of "show, don't tell." In the revised version, it's never stated that the girl is sad, but you can kind of figure it out from the other information provided.
It's very subtle, but if you compare the two examples Azurne gave, you can see that in fact they illustrate
completely different principles. Or consider Phoenixsong's thunderstorm example: "Lightning flashed across the sky, illuminating his surroundings for just a heartbeat before everything faded back into inky blackness." This
implies that it's a) storming and b) nighttime. But you could do exactly the same thing by writing something like, "A shattering crash brought him awake in an instant, his heart pounding and eyes straining against the black," and that doesn't talk about the sky or the storm at all.
A great example by someone way more talented than me is this, an excerpt from Terry Pratchett's
Night Watch:
Boards had been nailed over the tiny window at street level. This wasn't a place where light was welcomed. And all the walls, and even the ceiling, were padded heavily with sacks stuffed with straw. Sacks had even been nailed to the door. This was a very thorough cell. Not even sound was meant to escape.
A couple of torches did nothing at all for the darkness except make it dirty.
Behind him, Vimes heard Nancyball throw up.
In a strange kind of dream, he walked across the floor and bent down to pick up something that gleamed in the torchlight. It was a tooth.
This scene is all about telling, not showing. What's it showing? "Horrible things happened in this cell." But it's powerful for the very fact that this is never stated outright. Especially that last sentence, "It was a tooth." What a punch in the gut! You wring so much dark and sinister out of that understated little sentence that would be difficult to manufacture even out of a couple of paragraphs describing exactly what
did go on here. Or take perhaps the champion example, one you've probably seen before, from Hemingway:
"For Sale, Baby Shoes, Never Worn"
The "tell" version of this story would be (in extremely brief, it's much more nuanced than this and there are many different interpretations--thus showing how powerful the concept of "showing" or, more accurately, "omitting" is) "She was going to have a baby, and then didn't." The show version has essentially no description. It conveys three facts. But when the reader processes it, they can spin an entire tragedy out of those six words. It's the same thing that's going on with "she was sad" versus "three days later, she still wasn't eating, and even a visit from her best friend couldn't draw out a smile", but if you're framing "show, don't tell" as necessarily involving description, you would probably miss it.
So, the tricky thing about "show don't tell" is that, taken to its extreme, you're showing absolutely nothing at all. Kind of an unfortunately-named concept imo.
It's not that it's a
bad change ("he slew the dragon" to the brief scene); it's just not a case of telling vs showing.