X11 is, by design, a networked GUI environment. This means that an X11 client can live on a machine that is different from an X11 server. Generally speaking, an X11 client usually requires more processing power, whereas an X11 server is merely interpreting X11 messages and rendering graphical elements on the screen.
This design makes it possible to use a single powerful computer to run intensive X11 client programs, such as particle simulation, office productivity suite and etc. End users will then use inexpensive machines as X11 servers. In other words, an X11 server is somewhat like an SSH client (PuTTY).
One can also expand on this idea, and have a single X11 server (graphical terminal) connected to X11 client programs running on several power machines.
The separation of client and server make system administration a little easier because only one update is needed on the machine running an X11 client. For example, when a new version of OpenOffice becomes available, only one update is needed. Then, anyone who starts this X11 client from other computers will automatically be running the new version of OpenOffice.