Originally posted by Guv
Static electricity can build up on the screen and cause minor problems with the image. The degauss button does something to get rid of the static electricity.
Monitors generate large magnetic fields; over time these fields can build up and distort the shadow mask or aperture grille and therefore affect picture (particularly the colo(u)r of the picture). Other magnetic items, unshielded speakers, can also generate fields that distort the picture. Televisions auto degauss on a cold start.

Cleaning your screen with a duster or a damp stocking or whatever will remove static but not magnetism.