To remove magnetism from a device. The term is usually used in reference to color monitors and other display devices that use a Cathode Ray Tube (CRT). These devices aim electrons onto the display screen by creating magnetic fields inside the CRT. External magnetic forces -- such as the earth's natural magnetism or a magnet placed close to the monitor -- can magnetize the shadow mask, causing distorted images and colors.
To remove this external magnetic forces, most monitors automatically degauss the CRT whenever you turn on the monitor. In addition, many monitors have a manual degauss button that performs a more thorough degaussing of the CRT. You can also use an external degausser that degausses the monitor from the outside. Since it may be impossible to remove the external magnetic force, degaussing works by re-aligning the magnetic fields inside the CRT to compensate for the external magnetism.
You can also degauss magnetic media, such as disks, which removes all data from the media.
Also see Northern vs. Southern Hemisphere Monitors in the Did You Know . . . ? section of Webopedia.