Okay: Show, don't tell is a shorthand way of describing a whole range of techniques. The concept connecting those techniques is the idea that you want to make your reader's brain engage, to become an active participant in creating the world of the story. That engagement is what makes the story come alive for them; their own brain's activity is the difference between a story that galvanizes them and one that falls flat for them.
Here's a short list of techniques (probably not the only ones) that constitute showing rather than telling:
1) Dramatize the scene instead of having a character report what happened.
2) Force the reader to vividly imagine a sensory detail instead of informing them of what is true.
3) In dialogue, imply more than what is being said in words, so the reader must infer the rest of the truth for themselves.
4) Force the reader to put together clues to realize what happened, rather than telling them what happened.
Examples of the above:
1) Dramatize the scene: Instead of having a character drag their friend back to the cabin and proclaim, "Joe was shot!", include the scene where Joe gets shot.
Informing the reader of facts (telling) is fast, and sometimes appropriate, but it doesn't engage their brain and therefore you risk losing their interest when you do too much of it.
If the scene is unimportant (or would betray truths you want to hide from the reader for now), then go ahead and "tell" them what happened. If what happened is actually important to the story, however, then always plunk your reader down in that moment and make them witness it for themselves.
2) Force the reader to imagine sensory details: Instead of you, the author, saying, "Joe was shot and fell over", say something like, "Joe jolted backward as a spray of blood exploded from his shoulder. He windmilled into the grass."
The goal is to make the reader see this scene in their head. Informing them of facts won't do that, because their brain will do the minimum required to understand what's going on, and if it has all the facts, then it doesn't need to go to the extra effort of imagining anything. You want to force it to imagine the scene, so don't tell it facts; show it details it must put together into a scene.
I find focusing on strong verbs and nouns, as opposed to strong adjectives and adverbs, helps trick the brain into imagining the scene. I think the reason why is that it's a less common way of describing things, so the brain is less adept at figuring out what you mean. Therefore, it has to do a little extra work and imagine the scene.
As an example, I believe "dark clouds completely blocked the sun" is less likely to make the brain picture the scene than "stormclouds walled off the sun", even though the two sentences are trying to convey the same thing. The second phrasing is a little rarer to see in writing than the first, so the brain has to engage a little more.
3) Imply more than what is said:
"I don't want that stinking music at my party," said Gurpreet.
Emily turned to him, her eyes hooded. After a moment's regard, she said, "And what, exactly, is so stinking about it?"
The goal here is to avoid saying explicitly what Emily is thinking, and to instead imply it. There's nothing in the text above to explicitly say she's taken exception to what Gurpreet said, but it's implied.
When you imply information, the reader's brain has to work more to figure out what is going on. That slurps them into the story more effectively because they have to be mentally engaged and alert to the details in order to follow the narrative.
4) Force the reader to put together clues: For this one, I'll use an example. In the book The Life of Pi, the majority of the novel consists of a several engaging and beautiful stories, from the narrator's childhood and from his recent history. But some of the details aren't very believable, and also the personality of the narrator described by the stories doesn't match up very well with the narrator who is actually telling those stories. It's only at the end of the book you realize the narrator is unreliable, and he is telling you the beautiful stories because the truth broke him and he can't face what actually happened.
It's a very slow process, but the book builds you up to this realization with skill by feeding you just enough dodgy-sounding stuff amid the wonderful stories to tingle your bullshit-detector without totally setting it off. At the end of the book, a handful of new clues allow you realize what all the preceding clues meant, and your brain finally unlocks the puzzle of what was really going on. This makes for a much more satisfying experience than if the author had the narrator exposed by another character as a liar. Your brain figured the mystery out; it wasn't figured out for you and then spoon-fed to you.
As others have said, telling is a valid technique. It's only that telling risks losing you your reader's engagement, which is all that's pulling them along through your story. Showing helps keep the reader's brain engaged and working.
(As an example of when telling is completely appropriate, it's common in mystery novels for the detective to explain who the killer was at the end. This is fine, because the reader just spent the whole book trying to figure out what happened. They stayed engaged for the entire story, and the author doesn't need to hang on to their attention for much longer, so it's fine for the author to simply satisfy their curiosity and wrap up.)
For me, personally, the most helpful thing on the road to learning to show instead of tell--i.e. to find better words to use as I wrote--was the nouns/verbs thing I mentioned earlier. Try to strip out adjectives and adverbs in favour of stronger nouns and verbs; make a game of it. Once you've learned to do that well, you'll be able to add the adverbs and adjectives back in judiciously, where appropriate, because you'll have acquired stronger technique. Just remember the goal is to paint a vivid scene into your reader's head; you have to make their imagination engage, and not simply convey information to them.
Best of luck!
