Normally with X, it's easy to run an application on a remote computer just by using X forwarding:
local:~$ ssh -X host host:~$ echo $DISPLAY localhost:20.0 host:~$ xterm
xterm will appear on your local computer.
But if you want to continue working with that application on a different remote computer (or once you are physically in front of the computer it is running on), then you're out of luck.
For an application running in the terminal, you can start it inside
a GNU Screen (or
tmux) session which you can
detach and then attach to again on another
GNU Screen for X
X Persistent Remote Applications) lets you
move graphical applications from one computer to another in addition
to fixing other problems with X forwarding.
If you instead use
xpra for the forwarding, then you can detach
and reattach to the session at will.