Compiz is a thing that can make your desktop look fancy; XGL is an X server, afaik, like Xorg, but an alternative. If you wish to enable, say, Compiz you'll need to get good drivers (from ATI, 'flgrx') for your card; the software renderer 2d drivers often offered ('radeon' for example) aren't usually enough. Keep in mind, though, that at the moment at least ATI drivers' DRI (Direct Rendering Infrastructure) doesn't work with Compiz, so you can't have them both at the same time as of now.
Try it out if you want to; there are guides on the web, I suggest following them since it might be tricky at times to get Compiz (for example) working. Last time I tried, though some time ago, took half a day. First get ATI's drivers installed and working all right, then go on with getting a good guide on how to set Compiz (and probably XGL) working and how to enable/disable them.