If you've never heard of the X Window System then the first thing to realize is that it has absolutely nothing to do with Microsoft Windows.
Rather, The X Window System (more commonly known as X or X11) is a computer software system and network protocol that provides a graphical user interface (GUI) for networked computers. In a nutshell, it enables you to build GUI environments such as by drawing and moving windows on the screen and interacting with a mouse and keyboard.
Since it's an open source project, there are many implementations of The X Window System and Apple X11 is the most popular implementation of the X Window System that makes it possible to run X11-based applications in Mac OS X. It's based on the open source XFree86 project which is the most common implementation of X11. Apple X11 includes an X11 window server, Quartz window manager, libraries, and basic utilities such as xterm.
You'll need to be well versed in network computing and programming to work out how to use Apple X11 but you can be at least assured that this is the most important implementation of The X Windows System on the Mac.
