X11 is the X Window System which allows you to run software on a UNIX/Linux server in a Windows-like way such that you can use your mouse to click around in it. The secure way to do this is to forward your X11 packets through your ssh conection which automatically sets your DISPLAY environment variable for you. Manually setting your DISPLAY environment variable opens your computer up to security risks.
- Invoking Applications on a Research Computing Server from a Microsoft Windows Computer
- Invoking Applications on a Research Computing Server from a UNIX/Linux/Mac OSX Desktop Computer
More on X11 at Wikipedia: http://en.wikipedia.org/wiki/X11