X Window: A Definition
The X Window System (referred to as "X" or as "X Windows") is an open, cross-platform, client/server system for managing a windowed graphical user interface in a distributed network which was the result of research efforts in the early 1980s at Stanford University and MIT, to develop a platform-independent graphics protocol. MIT has placed the X-Window source code in the public domain, though, managed by the X.Org consortium. Being an open standard, the X-Window system makes a particularly attractive system for Unix vendors, and almost all Unix graphical interfaces, including Motif and OpenLook, are based on X-Window. Although Microsoft has its own platform-dependent windowing system (an integral part of the Windows operating systems), there are vendor-supplied X Windows products that can be installed to run on these Windows systems.
What is an "X-Window?"
Technically:
A specification for device-independent windowing operations on bitmap display devices, developed initially by MIT's Project Athena and now a de facto standard supported by the X Consortium. X was named after an earlier window system called "W." It is a window system called "X", not a system called "X Windows."
X uses a client-server protocol, the X protocol. The server is the computer or X terminal with the screen, keyboard, mouse and server program and the clients are application programs. Clients may run on the same computer as the server or on a different computer, communicating over Ethernet via TCP/IP protocols. This is confusing because X clients often run on what people usually think of as their server (e.g. a file server) but in X, it is the screen and keyboard etc. which is being "served out" to the applications.
X is used on many Unix systems. It has also been described over-sized, over-featured, over-engineered and incredibly over-complicated. X11R6 (version 11, release 6) was released in May 1994.
Source: http://hostingworks.com/support/dict.phtml?foldoc=X+Window+SystemRealistically:
X is a way to integrate graphical Unix applications into a windowed system through a terminal program. In X, the client-server relationship is reversed from the usual. The remote computers contain applications that make client requests for display management services in each local client workstation. X Windows is primarily used in networks of interconnected mainframes, minicomputers, and workstations. It is also used on the X terminal, which is essentially a workstation with display management capabilities but without its own applications.