VNC is a technology that allows one to access their desktop remotely, similar to the Microsoft Terminal Services client. If your computer runs a "VNC server", then you will be able to connect to it from other machines using "VNC clients."
The default Ubuntu desktop comes with a simply configured VNC Server. This can be accessed through System Menu > Preferences > Remote Desktop. However, the configuration described below provides a server that provides far better performance.
First, get the right packages
% sudo apt-get install vnc4server
This gets you a 'vnc' module for your xorg X server, which can export an X session as a vnc host, and also let you use it on your local display as well (unlike Xvnc and vncserver commands).
Once you've installed the packages, you need to edit your /etc/X11/xorg.conf. In your "Module" section, add the line:
Load "vnc"
In your "Screen" section, add the line:
Option "PasswordFile" "/root/.vnc/passwd"
Now you need to create the actual password file. You need to switch to root and run the realvncpasswd utility:
% sudo su % realvncpasswd (enter password)
You should be all set. Restart your X server and give it a shot.