The LARP entry on Wikipedia has a really good, concise definition:
“A live action role-playing game (LARP) is a form of role-playing game where the participants physically act out their characters’ actions. The players pursue goals within a fictional setting represented by the real world, while interacting with each other in character. The outcome of player actions may be mediated by game rules, or determined by consensus among players. Event arrangers called gamemasters decide the setting and rules to be used and facilitate play.”
For more information, including common terms and answers to a lot of frequently asked questions I suggest looking over the Wikipedia entry on LARP and this article I wrote as an introduction to the hobby.