You often need to use a graphical application directly from the server. The main example is a browser.
You can install Firefox on the server with minimal dependencies, but - who knows why - having connected your home computer to the server with ssh -X... is not enough. You have also to launch firefox with firefox -no-remote. And beware where are the files dowloaded stored (chance is it's on your home computer, not on the server).
You can as well use Firefox on your desktop but make is go through your server. Using your server as proxy allows you to make the Web site opened by Firefox think FF is run on your server. To do so, launch ssh proxy (ssh -D) then go on the proxy page of Firefox (on your desktop), gives localhost (better give the IP: 127.0.0.1) to have it run using your server as a proxy.
The exact ssh syntax may be:
ssh -fND localhost:$PORT
Localhost may be 127.0.0.1 (or you can make sure 127.0.0.1 is given the localhost name in /etc/hosts), and port can be nearly anything between 10000 and 20000.