Most Linux users use the X Window system, which is designed to transparently export graphics over a network. A user on machine1 can fire up X-Windows and connect to machine2, and run programs, see files, and so on just as if they were directly in front of machine 2, even if machine1 is in California and machine2 is in Switzerland.
Even if all you have is a terminal emulator (e.g. Hyperterminal, Procomm Plus, or one of the many terminal programs for Linux) you can log in remotely and run non-graphical, command-line tools just as if you were at the command line of the remote machine.
This is extremely useful for remote administration. If you're a webmaster and your webserver is having problems, you don't have to go in to work, you can dial in to the server from home and do everything that you could do if you were in front of the machine. (Well, okay, you can't swap hardware, but just about everything else.)
In the Windows world, these capabilities are imperfectly emulated with things like PC Anywhere or WinFrame. Each of these has limitations and applications that don't work with this model, and requires careful setup, because the applications were never intended to run in such a manner. Also, Windows often needs a reboot for even some trivial changes to take effect, which is in sharp contrast to Linux (see rebooting).
Note that there are X systems available that run under Windows, so even Windows boxes on the same network can run Linux programs. At least one X program is free.