Roleplaying games--by which I here mean pen-and-paper roleplaying games or tabletop roleplaying games--are games of collaborative storytelling. You sit down and tell a story together. The only limit is your imagination and your expressive vocabulary.
But obviously, just sitting down and telling a story together can be very chaotic. What will the story be about? If two of the players disagree about what happens next, how do we decide between their ideas? Can everybody contribute anything they wish to the narrative, or will we give different players different powers and responsibilities? To answer these questions and structure the playing experience, we use a set of rules, the roleplaying game itself.
Historically, the first roleplaying games divided the players into a Game Master (or Dungeon Master, or Storyteller) who thought up the fictional world and had final control over whatever happened, and the "players", who each controlled only a single character and could only tell what that character tried to do. This was of course hardly collaborative storytelling (although it did lead to some excellent games). Recent independent roleplaying game development has explored many alternatives to this division, with often brilliant results.
If you play one of the RPGs on this site, make it Shades. Although some of the others have been discussed more, they are often untested and not exactly meant to be played in a straightforward fashion. Shades, however, is a perfectly playable and yet very radical design that leads to a play experience you probably will not have found in any other game.