You're using two computers. You're using the X window system of the first to type to and look at. You're using the second to do some important graphical work. You want the second to show its output on the display of the first. The X window system makes this possible.
Of course, you need a network connection for this. Preferably a fast one; the X protocol is a network hog. But with a little patience and suitable protocol compression, you can even run applications over a modem. For X protocol compression, you might want to check out dxpc http://www.vigor.nu/dxpc/ or LBX http://www.paulandlesley.org/faqs/LBX-HOWTO.html (also known as the LBX mini-HOWTO).
You must do two things to achieve all this: