X-11 is the name of the 'window manager' used for most Unix and Linux operating systems. A window manager is software that interfaces the video, keyboard and mouse drivers together to enable the user to communicate with the computer via a graphical user interface (GUI).
What makes X-11 unique is that it is designed to run over a network connection, specifically over Internet Protocol. This enables a remote user to use his local X-Windows environment to interact directly with the other computer's window manager as if he is sitting on that machine.
X-11 uses a client-server model, where the window manager is the server, and the user is using various clients. Applications that can be run in the graphical user interface are often written to use the X-11 software libraries to enable them to be used remotely. This is one of the strengths and power of the Unix system. X-11 enables a remote system to treat your local computer, it screen, keyboard and mouse as just another set of terminal interface devices that use an X-11 driver to communicate with the X-Windows manager.