X server
A process, in an X Window System which controls a bitmap display device and usually also a keyboard and mouse or other pointing device. The X server performs operations on request from client applications, which may be on the same computer or a different computer connected via a network.
Note that typical client-server architectures do input-output on the client and processing on the server whereas in X the terms are reversed as the X server is serving IO rather than processing resources to the application.
If the two computers are not both Unix machines (e.g. one is a Windows machine running VNC) or if a more secure connection is required (e.g. tunneling with ssh), the clients may talk to a proxy X server that forwards the requests to another machine where the real IO takes place.