Live Roleplaying is a mixture of improvisational theathre, carneval and "cops and robber" games.
The players take the roles of imaginary characters and play these roles for a certain time. Unlike in a real theatre, there is no fixed script in arole playing game. Instead the players decide, what their characters want to do and then actually act it out live.
The goals of each character are determined by his background. Each player creates a background story for his character with information about his past and his goals and desires. In doing this he usually cooperates with the directors so that the final character will fit in the framework of the background that the directors have created.
This background, also called a campaign or Story provides the framework in which the characters act. It usually is an imaginary world, based on real world concepts. For example the Vampire game assumes a background of a world, very similar to our own, but with some fictional, supernatural elements (vampires) included.