From LXF Wiki
A window manager is a program which controls the layout of program windows on your screen. It provides title bars, resize controls, and other features necessary to manage windows. Without a window manager, your programs would just appear as boxes on the screen -- no title bars, no controls.
In UNIX/Linux, a window manager usually works with the X Window System.
The desktop environments GNOME and KDE include window managers (Metacity and KWin respectively), although in normal conversation a window manager is distinct from a desktop environment. Whereas a window manager provides the basic window control functionality, a desktop environment provides a programming base with libraries, bindings, subsystems and more.
Most programs will run under most window managers, although there are exceptions.
Some window managers: