For example: let's say a character in your novel is angry for some reason. Perhaps she missed the bus to work due to passing through a space-time wormhole, something like that. Now, the poor man's way to express this anger on paper is:
"She was angry that she missed the bus."
BORING. In moments like these the reader really needs to get under the skin of the character, especially if it is a principal character. So, for example:
"Hot fury flushed her face, veins popping on her neck as she kicked the bus stand."
Now we're talking...or should I say, 'showing'! Here, the reader is sharing the same headspace as the character and is being exposed to how she is angry. It makes for a more visceral experience, and deepens the connection between reader and protagonist.
If that's what you want, of course. Depending on the tone one is after, it may be that you're deliberately holding the protagonist at arm's length from reader empathy: you're not supposed to know how they feel. That's fine, and frankly you don't want to be fleshing out every minute emotion and thought-process to your reader because you run the risk of over egging it and exhausting your reader in a way similar to purple prose. Having said that, showing is still better than telling here: if you tell your reader what is going through the protagonist's mind, we're exposing them to what can only be described as dull description, the kind to be found in encyclopedias and plaques describing museum artifacts. Telling informs, but showing invites. With showing you can build that essential connection between the page and the reader's imagination that makes them want to keep turning the page. Showing brings your characters - and story - to life.
And that means one has to avoid pulling out the character's CV whenever they first step into the story. Picture this: a family are excitedly bustling about a house, preparing food. The mother's hands tremble with terrified excitement over a hot stove. The father's hands appear from the hands, firm, steady, holding hers in his own. They meet each other's misty eyes. They smile.
Then, with a click of the door, all eyes turn to the entrance as a young man in a soldier's unifrom steps inside.
Now, at this very moment, what you shouldn't do is hit the pause button on the narrative and launch into a detailed description about Soldier Sam, what each of his badges mean, how he just came back from years of service in Afghanistan, how he got that scar on his left arm, how the last time he'd spoken face to face with his parents had been an argument and how he'd spent every night since then fearing that he'd never get the chance to apologize.
Are these facts about Sam important? Perhaps, but this is a terrible way to present them. Prior to his arrival we have this emotional build up, and a sense of pace. Yes, even cooking has a pace in the narrative because something is happening. When Sam steps through the door and the narrator steps in to monologue about him, everything grinds to a halt. Any emotional resonance this scene could potentially have had is destroyed: imagine if you're about to witness a long overdue reunion scene in a movie, and just before they embrace in a hug you pause the movie, pull up the Wikipedia page on one of the characters to read up on their background, then after five minutes you hit the play button again. It doesn't have any of it's desired effect any more, does it? You have just robbed that scene of its purpose.
Much better that the story keeps pushing forward and these facts about Sam are threaded seamlessly into the narrative. You can show Sam scratching his scar as he nervously watches his mother chopping with the kitchen knife, for example. This intrigues the reader, and hints at something bigger at play here, something more than meets the eye. And this gets them wanting to kow more - in other words, they keep turning the pages. Then, when opportune moments arise and we can fit it into the narritve, we can reveal these facts about Sam's personality and history when they become relevant.
How one presents such character facts and revelations is a challenge unto itself, mind: flashbacks and extended dialogues can be effective but when used ineffectively can be a blatant infodump. Take, for example, a conversation between two detectives on a stakeout, sitting in a car outside a suspect's house. Suddenly one detective needs a full rundown of the whole case and the suspect's profile right there and then - except, no reader will believe that for a second, as it's obviously done for the benefit of the reader to bring them up to speed. It's a slightly more subtle way of the narrator monologue desribed above, only here an in-story character becomes the mouthpiece. While the pacing is less damaged this way, this ham-fisted method can still shake your reader's suspension of belief. Besides, if these backstories and catch-ups are so intersting and necessary to your story, why aren't they in your main story in the first place?
Show don't tell is a simple but powerful way to bring energy and power to your writing, and can really bring your characters to life. If you find yourself pausing mid-writing, wondering how to explain something to your readers, stop. Think of it in another way: how can I show this to my readers?