Virgin Games consist of grabbing Virgins from the audience, usually at random but occasionally targeting friends, and persuading them to do something silly, sexual, or most likely both.
The reasoning behind the Games varies, but generally it's because it's fun, it's funny, it's a simple rite of passage that everyone's gone through without having to do anything difficult, and because messing with people makes for good entertainment.
Most casts have a tradition of playing Virgin Games before actually showing the movie. Tolls of Madness, for example, normally has the people playing Trixie run a few Virgin Games between the preshow and the actual performance.
Refer to the Virgin Games List for ideas regarding Virgin Games.