"Show, don't tell" is the cardinal rule of writing, and it's true for telling stories too.
Telling is when you say something like, “And then, he did the funniest dance – it was so hilarious.” It's telling because I can't imagine what you're describing, so your words don't inspire an emotional response in me. You told me the dance was funny, but it doesn't feel funny to me as the listener.
But if you say something like “And then he waved his hands above his heads, and gave these short, stiff jumps like he was popcorn being popped” now you're showing – and that means that I'm much more likely to be able to tap into the humor of what you're describing. I can imagine the scene in my head and that imagined scene is almost as funny as being there in person.
In other words, showing is when you give me everything I need to imagine the scene.
Unfortunately, this creates a problem. Showing takes time, and if you show every little thing that happens in your story, the story will quickly get long-winded. So what's the solution?
Simple. Show the scenes or details that matter to your story.
If you are telling the story of how you survived a shark attack, you don't need to “show” how relaxing the water was before the shark attacked – but you had better show how you dramatically fought off the shark!
Also, make sure you don't repeat details. If you're telling the story about how you talked with a super cute girl, it's natural to mention how good she looked over and over – but it's not interesting for your audience. Your audience will be tempted to tune you out unless you keep serving them interesting new details.
The bottom line: share a detail once (twice, tops) and then move on to something new. If you repeat details, you'll easily stray from showing into telling.
Next: Use Vivid Details, Not Lots of Facts