The Xcomposite extension adds functionality to the X server to allow windows to have their output redirected to internal memory locations, rather then the screen.
The compositing manager uses the composite extension to manage how windows are drawn on screen, for example, its usually used to combine overlapping windows to archive semi-transparency (see thru windows), or can add shadows to windows. Since its the manager that determines what will be drawn on the screen, the actual possibilities are not necessarily limited to simple transparency and shadows.
The original composite manager(s) where incredibly slow, due to the fact that they processed all graphics operations on the CPU, this ment that the screen might look nice, but feel incredibly slow. Compiz and Beryl (or whatever they are called) combine new extensions (or features, as the case may be) with the Xcomposite extension to allow them to make use of 3D acceleration to perform their graphics effects, so they are not necessarily slow. (see AIGLX and Xgl in the wiki)
Neither of the two are related to any specific hardware (the X server needs a display, such as a video card, and the Xcomposite extension only needs a CPU and RAM), unless, of course, you combine them with 3D, then the 3D graphics card can be used.
(see instructions on how to install and use the ATI drivers for information about installing/using them. As it stands, im not sure how useful "AGP ATI video card" is to modprobe'ing it).
Last edited by SciYro; 09-05-2007 at 04:40 PM.