Though matociquala clearly says at the start that it can be used in two ways, the discussion in the comments made me realise that confusion between these different meanings can lead to a lot of debate in which people end up talking at cross purposes, so I thought I'd try and offer a few examples based on my experience teaching an introductory fiction writing course.
One instance where people use the shorthand "show versus tell" is the first meaning that matociquala mentions in her post. It relates to the different ways of writing parts of a story. Should you show it as a complete scene with dialogue, actions and description, or should you use a narrative summary? Actually, this meaning is probably better phrased as "dramatise versus narrate". (This is the way it was put on one of the OU courses I took and zeborahnz also refers to it in the comments.). In competent hands, both dramatising and narrating are perfectly valid techniques and great fun can be had trying to work out which parts of a story should be dramatised and which narrated.
When it comes to beginners, however, they will often summarise, even when it's obvious that the action should be shown fully dramatised. A common reason for this mistake -- and the easiest to fix! -- is that they are trying to squeeze a story into too small a word count. The story often starts out OK, but by the middle, it's starting to read like a synopsis. On creative writing courses, the word counts can be very tight, as low as 1000-1500 words. There is often the option to submit the opening of a longer story, but rather than do this, new writers may resort to narrative summary in order to keep the whole thing within the word count. It can also happen in longer stories where someone is trying to remain within a word limit for a magazine or competition.
Knowing how long a story ought to be is not an exact science, though I've finally developed something of a feel for what works at different lengths. Anyway, the answer to fitting a story into a given word count is never just "summarise the plot to make it fit." Instead, try teasing out the most important elements of the story and focus on those. Removing any "Dwarves drinking soup" scenes will help. If that fails, use another story!
Another reason for writing in narrative summary is that the writer has the story running in their head like a film in glorious Technicolor. However, they have failed to realise that in order to transfer the scenes to the page effectively, the writer has to provide detail. Instead, they slip into the sort of telling mode that they would use to describe the plot of a TV drama to a friend who had missed that episode. For example:
Jim went upstairs and found Pamela's body lying in a pool of blood. He was distraught. It was obvious that Dave had shot her and run away. Fighting back tears, Jim drove to Dave's house, but Dave had already gone. Jim knew he had to get to the airport before Dave escaped. Driving like crazy, Jim just got to the airport in time. Dave was still at the check-in desk.
"You killed Pamela," he shouted.
"You never really loved her," Dave shouted back. "You didn't understand. I was the only one who really cared for her!"
Then Dave leapt on Jim. They fought viciously, but after a huge struggle, Jim used his karate skills to subdue Dave. The police arrested him and took him away.
OK, that is slightly exaggerated to make the point, but not all that much. I've had a lot of stories like this from my students over the years. The underlying story is fine and the prose is serviceable, but it isn't a vivid story. Is it set in London, New York or Leeds? How old are the characters? What do they look like? What sort of house does Pamela live in? It's just a sketch of a story, not yet a fully realised one. In this case I would explain about the difference between showing/dramatising and telling/narrating to encourage them to do better next time.
The other meaning of "show versus tell" is (as matociquala demonstrates) at the paragraph or sentence level. To be honest, I would say that both the examples she gives are "showing". I admit that in the second one we're just told that the character nods, but we (presumably) already have a clear picture of Kari from earlier descriptions, ditto the setting, so just to write "Kari nodded" is fine as far as I'm concerned and, as zeborahnz says in the comments, it's more a stylistic choice on the part of the writer which aspect of the scene they want to emphasise.
No, the sort of thing that gets me mentally shouting, "show don't tell!" while marking my students' stories goes more like this:
Jane lived with her older sister in a lovely house. It was a big house and it stood on a busy road, set back a little with a pretty garden in front and a path running up to the front door.
Jane felt happy that morning. She got up and dressed quickly and went down to the kitchen. Mary was already there, making breakfast. She was angry because she had just lost her job and felt bored sitting at home all day. She resented Jane because she was so beautiful and had an interesting job that gave her the opportunity to travel.
Now, as with anything in writing, if it's done deliberately and for the right story, such a simple style could just possibly be made to work, for example if one was trying to write a sort of modern fairy tale. However, that's not the case with the stories I have to mark. They are merely bland and everything feels generic. There's no distinctive detail to make the reader's mental picture feel real and vivid. How old are these sisters? Nineteen and twenty-two? Thirty-five and forty? Fifty and fifty-three? There's nothing so far to confirm or rule out any of these options.
One annoying problem with generic writing is that the reader (given nothing much to go on) starts to invent their own picture of the characters and scene, which is fine until a detail finally shatters this image and the reader has to re-invent everything they've pictured so far. How old did you assume Jane was? If you thought she was say about twenty-five and Mary was a few years older, it would be frustrating to discover in the next scene that Mary was complaining that, at her age, so near to retiring, it was almost impossible to get another job.
So, even though this wasn't just a plot summary like the first example, the writer still needs to add much more detail about what type of house they live in and what the sisters look like. Actually, one thing that might improve this example would be a firmer grasp of viewpoint and a tighter focus on one of the women, but even if it's staying as omniscient, the reader needs to see how Mary's anger makes her look and behave. It may be that the writer hasn't chosen the best scene to depict. It would probably be better if the story started with Jane coming home from work tired and finding Mary watching TV in an untidy sitting room and with the breakfast dishes still unwashed in the kitchen sink. Immediately we're getting some detail of their lives and the way each woman reacts and the ensuing conversation between them will tell the reader a huge amount about their personalities and the current situation.
To be honest, I never just write "show don't tell" on a student's story. It's not helpful because, as this post shows in its long and rambling way, it's too vague. It's another example (like my bête noire "murder your darlings") of a piece of writing advice that is fine when given to one particular writer in relation to one particular story in a situation where both of you know what is meant, but is useless when applied as a One Size Fits All instruction.