"Show, don't tell" is one of the rules of thumb of proper storytelling in a visual media (such as movies, TV series and comics). It means that, in general, it's better to show something happening rather than just telling what happened. It can apply even to written stories, where it means that the events should be "shown" as a narrative, rather than being explained.
This is not, of course, a hard rule. Sometimes it's better to just tell something as a quick summary rather than going to the lengths of actually showing the events in full. Too much "showing" can actually be more boring than just quickly telling what happened.
What grinds my gears is when people use the "show, don't tell" argument to criticize works of art in situations where it really doesn't apply.
There are excellent examples of things not being shown, just hinted at in dialogue. For example, consider the famous "hamburger scene" in the movie Pulp Fiction. The dialogue, and in fact the whole situation, makes reference to those people having screwed up Marcellus Wallace somehow, yet we are never shown what happened. We are only told that it happened. However, we don't need to be shown. In fact, the scene would actually not be as good if it spent time showing what happened, rather than just telling about it through the dialogue. As it is now, the scene is just superbly done. (In other words, rather ironically, the scene becomes better when it does not blindly adhere to the rule, and instead breaks it.)
I think that sometimes people use the "show, don't tell" as an excuse to criticize a work of art that they don't like. For example, an acquaintance of mine criticized the speech made by the Architect in the second Matrix movie for breaking "show, don't tell". I honestly cannot understand what exactly he was suggesting. I think the speech is just spot-on and does not need any "showing". (I brought up the Pulp Fiction scene as a counter-argument and, according to him, that was different. I was unable to get a clear explanation of why.)