Within the X window system, a special application called the window manager is responsible for managing application windows and application-independent behaviour such as popup menus appearing in the background.

You can even set up X to change its look and feel on the fly by changing window managers while the session is running.

In X, the window manager is the most important part, but not the only part, of an integrated desktop environment such as OpenWindows, CDE, KDE, or GNOME.

Probably over a hundred window managers have been written, and at least 20 have enjoyed lasting popularity. Some popular ones that I've tried myself:

Next time, before you say "I've tried them all, and my XXX is the best", take a look at Matt Chapman's extensive overview: www.plig.org/xwinman.