If I have a hard time dissecting showing directly, then I just simply ask about the end result: What showing wishes to create in the readers?
It is the difference between being told something is true, and experiencing that same something.
IRL, suppose I tell you my ten year old niece Katy is a piano prodigy. You feel one way about that, perhaps impressed, perhaps doubtful and thinking I am a doting uncle that heard her play Chopsticks.
Now suppose instead of telling you, I say "I want you to hear something, come with me and play along." I bring you to Katy's house, and I tell her your favorite piano piece is Mozart's Sonata #6 (One of his most difficult). She says, "Oh No!" Then grits her teeth, composes herself, and plays it flawlessly from memory. Now, IRL, how do you feel differently about the statement that Katy is a piano prodigy?
In fiction, "TELLING" is reciting some facts, like "John is crazy in love with Linda." Told facts are weak, they are easily forgotten by the reader, because the reader is not emotionally invested or feeling anything about the fact.
"SHOWING" is demonstrating, in one or more scenes, the consequences of the fact. If John is "crazy", show me some of the crazy things he is doing. What risks does he take? What responsibilities does he shirk? What friends does he stand up? How restless is he, when Linda is not with him? What does he DO because he is "crazy in love"?
"SHOWING" is giving the reader an experience, in their imagination, and this causes them to invest emotion in the fact and know what you mean. It puts flesh on the bones of "John is crazy in love", or the villain is "cruel" or "heartless", or "the mountain was impressive." All of those are tellings, not scenes. Darth Vader choking his incompetent soldier is "showing".
Of course in print everything is 'told', but that is misinterpreting the advice. It means do not label how they feel, show it. Do not inform us that Mary is extremely attractive, show us how people react to Mary because she is so attractive. Don't tell me Mike is a great car salesman, show me Mike selling cars --- Or if you don't know how to be a great salesman, show me another great salesman admiring or griping about Mike.
"I used to be number one in this shop every month. Last month I busted my ass and sold twenty-four cars, my all time high, and that bastard Mike sold twenty-six. That's frikkin impossible, dude."
Showing means giving the reader an experience (in their imagination) that cements the information you need them to know to understand the plot. It may take ten times as many words, or a hundred times as many, but these little experiences are the reason people read stories, because the author provides them with this kind of "assisted imagination" that lets them relate to characters and feel they are in the story, with the heroes, struggling to accomplish the goal and save the world. Even if "saving the world" this time is just getting Brittany married on Sunday without any major disasters.
Showing instead of telling has several advantages, though which apply depend on the context. I'll list several off the top of my head, based on my experiences of what showing achieves:
- You can be less repetitive, e.g. if the reader infers who spoke instead of you having to say "said X" on every line of dialogue;
- A lot of humour derives from the reader inferring what was meant;
- If I tell you a character has a trait without saying what makes that so or knowable, I've been vaguer and given you less of a picture of the story's world;
- If I tell you a character feels a certain way instead of conveying it in their behaviour and body language, I'm missing the latter's storytelling opportunity (plus imagery helps stoke the reader's imagination);
- Showing can be more economical in the sense you can show multiple facts about characters, e.g. people's reaction to a woman's entrance can prove both her beauty and their recognition of it;
- When you show you often can't help but be more inventive in the way you phrase things, which makes your writing more distinctive.
Other people will probably mention some other advantages.