The Composite Extension of the X Window System renders the graphical output of clients "...to an off-screen buffer. Applications can then take the contents of that buffer and do whatever they like. The off-screen buffer can be automatically merged into the parent window or merged by external programs, called compositing managers."[1]
This enabled the creation of compositing managers for X, capable of effects like transparency, 3D rotation, and jiggly windows.
The composite extension was added to X.org in version X11R6.8[2] in September 2004.[3]