VNC lets you use a computer remotely. If you have a recent Linux distro, VNC is what drives the "remote desktop" feature. This lets a VNC client connect to your X server. But you can also use VNC even if you aren't using the main display console of a machine.
When used standalone, vncserver starts what appears to programs to be an Xserver that they can run under, but it doesn't really connect to a screen, keyboard, or mouse. You then use a viewer program to see the state of the VNC session. Unlike X windows, viewers can come and go as they please without disturbing the session. So you can access your VNC session from anywhere without restarting all your programs.
Here's the Official Site. They don't make it particularly obvious, but there is a free version available for download (lacking only a few "enterprise" features that are rarely necessary). You can download the enterprise viewer for free. If you use Linux, look for a package in your distro called something like vnc4.
Here are instructions for tunneling VNC through SSH, but if you are running a recent viewer, it's easier to use the -via command line option.