If we want access to remote system then we will use ssh.
But what in case if we need run some program in graphical mode?!
If we run ssh with parameters 'C' and 'X'
-X is standing for X11 forwarding, and
-C is standing for compression of all data.
So, if we run ssh like:
$ ssh -CX user@host
$ is not part of command).
and then run program which we want, for example
$ nautilus &
After this nautilus process will be run at remote computer and window will be shown at the host computer.
For ssh without password look at this protip.