In computer terms, a windowing system is what handles drawing graphics to a computer screen. Depending on the OS and windowing system, this may mean anything from just being able to draw simple shapes (or primitives) to the screen and little else, up to allowing windows to be moved, resized, etc.

Microsoft Windows is an example of the latter. It has the advantage of having everything in one place, so all applications look and feel exactly the same. (That is, they all share the same toolkit.) But systems like this have the disadvantage of not being terribly configurable. (Among other things, in Microsoft's case... such as a lack of a real window manager, so windows cannot be moved or resized while they're performing a task.)

X11 (or just X) is an example of the former. In order to get real work to happen, one must also add a window manager. This means that an X desktop is extremely configurable, but it also means that there is no single toolkit, so not all applications work in the same way.