Compositing window manager
A window manager where each window renders into its own buffer and the final image is assembled separately — hence shadows, transparency and the end of redraw glitches.
In classic X11 every program drew directly onto the same screen surface, so moving a window left a hole that the program underneath had to repaint whenever it got around to it. The Composite extension, developed by Keith Packard around 2004, let windows render into off-screen buffers instead, which a separate compositor then stitched together, usually with OpenGL and the GPU.
xcompmgr was the first demo. Compiz arrived in 2006 and became famous for wobbly windows and a spinning desktop cube — an effect that sold Linux at trade shows and was then promptly switched off. Apple already had Quartz Compositor in Mac OS X, and Microsoft got DWM with Vista in 2007. In Wayland the compositor is the display server.