LARP stands for Live Action Role Playing. It's when someone literally plays the role of a fictional character while gaming. Still confused? Here's a handy guide to the practice, which depending on the player can be either awesome or creepy.
While LARPing is usually the domain of people who hook up in the real world for a bit of fantasy action, you'll also find your fair share of gamers getting in on it as well, especially if you play lore-heavy titles like World of Warcraft or Lord of the Rings Online. Hell, I even used to run into these kind of people playing X-Wing vs Tie Fighter.
Team Dynamite's comic book guide to the practice provides not only a fantastic introduction to the practice for anyone wanting to know more, but also enough self-referential gags that actual LARPers can hopefully see the funny side of things.