Compiz is a window manager that uses 3D graphics acceleration via OpenGL. compiz is quite popular because it has matured somewhat and it produces eye-candy desktops. However, they are situations where running a window manager other than compiz is more desirable. One reason for this is the lack of OpenGL capabilities on older computers. Another reason is that some of the compiz's visual effects can interfere with full-screen applications, such as games. For this reason, gamers often tend to switch off compiz prior to starting games. If you don't have compiz on you need to replace it with something else, eg metacity.