Mutter is a Wayland display server and X11 window manager and compositor
library.

When used as a Wayland display server, it runs on top of KMS and 
libinput. It implements the compositor side of the Wayland core protocol
as well as various protocol extensions. It also has functionality 
related to running X11 applications using Xwayland.

When used on top of Xorg it acts as a X11 window manager and compositing
manager. It contains functionality related to, among other things, 
window management, window compositing, focus tracking, workspace 
management, keybindings and monitor configuration.

Internally it uses a fork of Cogl, a hardware acceleration abstraction
library used to simplify usage of OpenGL pipelines, as well as a fork of
Clutter, a scene graph and user interface toolkit.

Mutter is used by, for example, GNOME Shell, the GNOME core user 
interface, and by Gala, elementary OS's window manager. It can also be
run standalone, using the command "mutter", but just running plain
mutter is only intended for debugging purposes.