Degaussing is the process of removing, or at least
randomizing, the
magnetic fields of a given medium or material. An
electromagnetic coil is used to put a much stronger field through the material than it already has. This forces the
atoms to realign from their old
magnetic field to this new one. When the field is moved, some atoms follow its movement and some do not, leaving the material's overall magnetic field in a fairly
random state.
One reason an object will have a problematic magnetic field in the first place is because it has been influenced by the earth's own magnetic fields. When this happens in computer monitors it can cause the electron guns to become misaligned, so the screen is blurry and discolored. Very old monitors (and TV's, for that matter) had to be degaussed by hand, by a technician who moved a hand-held coil over the screen and innards. Newer models have a button or option that discharges a capacitor into an internal coil for an instant degauss, and all modern CRT's do this every time they're turned on. The strong magnetic fields caused by using unshielded speakers near a monitor cannot be corrected by this instant degauss, so you must either have the device serviced or just ignore the problems.
Interestingly, the earth's magnetic fields will sometimes cause airplanes to become giant flying magnets. This plays havoc with their on-board compass, and makes the plane virtually unflyable. To correct this problem, a technician first removes all field-sensitive devices: computer, flight data recorders, sensors, etc. Then, the technician goes over the whole plane with a field sensor and coil, and degausses any magnetic "hot spots" on the chassis. This process is time-consuming, difficult, AND tedious, and is rightly loathed by most flight technicians.
In the case of magnetic media degaussing erases all data held by the medium, restoring it to a "like-new" state. Digital media (hard disk, floppy, tape, etc.) have to be formatted to usable again after degaussing, whereas analog media (various sizes of audio tape) do not. Degaussing is often required before businesses and the government will throw away obsolete or broken magnetic media, and the Department of Defense has strict specifications for equipment and procedure. Also, high-fidelity audio tape is very sensitive to noise, and hand degaussing can leave behind sonic evidence of how the degausser was moved over it. Because of this, any analog studio worth its salt will buy a bulk eraser with a built-in conveyer belt, to move the media through the magnetic field at a constant speed.