My explanation has always been....
RPGs are just like playing pretend when you were a kid. For some of you, it was playing "house," for others it might have been "cowboys and indians," or "GI Joe," or "Transformers," or whatever. You pretended you were someone else (or yourself, in a fantastic situation) and just let the other players in the game help create a story, or adventure, or just recreate what you think life should be like.
Unlike in some of those games, RPGs have a way to settle disputes on the nature of the imagined reality. In the case of Cowboys and Indians, I can say, "Bang! You're dead!" and you can respond "No, I'm not! You missed me!" and there's really no way for us to come to agreement - no bullet was fired, and neither of us is *really* dead.
In the case of the RPGs I play, the method of resolving such disputes is dice - like you'd find in a board game, though some sets of rules use special polyhedral dice (with sides more or less than six). If you say, "bang! You're dead!" in this kind of game, we roll dice to see if that's actually the case.
The only other real difference from playing pretend is that one of us is in charge of creating and maintaining the imaginary world and situations - rather than just having one of us say "there's a bunch of bad guys up ahead!" and then having the rest of us agree (or not), and then go from there, one of us can definitively say, "you see bad guys" or "you don't see anything."
I also have some fairly standard answers for some of the more common questions:
IS IT LIKE IMPROV OR ACTING?
Sort of, but you're not really doing anything to entertain an audience. You can do whatever you think is fun - you're just entertaining yourself, and maybe the other players. Also, the presence of the person constantly "setting the stage" means that you don't have to make up the situation (only your own actions) as you go along.
ISN'T THAT A LITTLE IMMATURE?
Maybe, but it's a decent way to pass the time. It's a lot more exciting than a lot of stuff, that's for sure.