Here's my definition towards Role-Playing:
Role-Playing, or RP as many of us calls it, is basically an storyline of mainly anything that you can think of by using your imagination and such. This is the most common question roleplayers get asked by non-roleplayers, and roleplayers alike: What is roleplaying all about? The problem is, it's not easy to explain the concept of roleplaying to someone who has never tried it. However, if you're looking for a brief description, how about:
Have you ever read a book or seen a film, where a character did something really silly, really stupid, and you thought, "No! Don't do that! You do *this* and..." or "If it were me, this is what I'd be doing in that situation..."
In a roleplaying, it *is* you. In many ways, roleplaying is very much like improvisational acting, but it's also a game where you have fun with your friends, and interact with them in a real social setting. It is quite ideal for everyone who would like to try your hand at acting as a hobby, but can't be bothered with learning scripts and all the other tools that go along with acting.
In short, it's basically you making up your own storyline and actions for your character. Regardless if they're fact or fiction and if the storyline follows up with the character or not.
This is just my definition though since many others got their own way towards what role-playing (Rping) really means.