In the Linux world, graphical programs can run on one
machine and display on another one. From the other side, we
can say that the user executes programs on remote computer
but they appear as they run locally, using the keyboard, the mouse
and displaying on the screen.
The program managing the screen, the keyboard and the mouse
is called the X server. It is called this way
because it allows several programs to share a single resource set
which is the display, the mouse and the keyboard. On a lighter
note, one can say that the X server allows several programs to share
the most expensive part of the network, the user :-)
This client server relation is very flexible. One can execute
programs on many remote computers at once and they will all
show on his screen, generally in rectangles called windows.
Further, he will be able to cut & paste seemlessly between them.