This portal talk about X Window System (also called X11 or X). Technical language could be used.
If you want to know how to configure your desktop in the simplest way, see DesktopEnvironment portal. Here you find advanced articles.
The X Window system is what gives many different Unices (including Linux) their graphical user interface.
The X window system includes everything that talks directly to the video card hardware. In simple terms, the X Window System provides to Unix a graphical user interface that allows a Desktop environment.
Unlike many other operating systems' GUI environments, X behaves like a server. This means that every GUI program that you run are clients and there is an instance of the X server running on your local PC.
One could draw parallels between using X and web surfing. In this case, the X server running on your computer is akin to a web server sitting on the internet while your program (eg. xmms) is like a web browser. The client program requests a resource (ie. screen real estate) from the X server and the X server gives the client access to the resource (provided that they are given permission with the xhost command).
Now, this may seem to be overkill but consider what can be made possible through such a system. You could run a CPU intensive program on a remote server with a more powerful CPU and simply instruct it to send all of the graphical output(ie. windows ,dialogs etc.) to your local machine's X server to be displayed on your local screen. This is generally done by setting the DISPLAY variable to "my_local_host_name:0.0" , which sends all of the information to my_local_host_name on screen 0 (there may be more than one X server running on a computer) and keyboard 0.
With this power comes some potential for security breaches. There are known cases where a remote hacker can grab keystrokes being sent over the local network or can even send keystrokes or mouse-clicks to an unsuspecting user's application.
(Somebody who knows how to lock down X could describe some of the ways to prevent this right here)
In the past, X was mainly responsible for doing any 2D drawing that was required. Now, X has been also given the capability of doing some of the 3D work as of XFree86 v4. This is done through an interface called GLX which is a layer on top of OpenGL with which many people are familiar. To make these 3D accelerated calls as fast as possible, Xorg now uses DRI (Direct Rendering Infrastructure) to communicate as directly as possible to the video card.
AtiHowTo - How to configure ATI driver (and 3D support!)
NvidiaGraphicsDrivers - How to configure nVidia drivers (and 3D support!)
tasksel - Provides task-based package management
WindowManager - Alternatives to a full-fledged desktop environment
XFree86 - The previous X Server (up to Debian 3.1)
Xorg - The current Debian X-Window server
XStrikeForce/FAQ - FAQ about the Debian X server