Anti-skid works to prevent a tire skidding by sensing the condition of each individual wheel (or sets of wheels, in some cases), and modifying the brake pressure being applied to that wheel.
The theory as bullethead explained is to prevent the wheel from actually skidding. If skidding occurs, directional control and braking efficiency is lost. A sensor in each axle of each wheel is connected to an anti-skid computer. If the computer senses that the change in wheel speed is incorrect (it stops turning, or turns too slowly), the computer directs a bypass valve in the brake line or system to divert brake fluid from the brakes on that particular wheel. This has the effect of decreasing brake pressure, and preventing the skid.
In theory, no matter how hard the pilot attempts to apply braking, the anti-skid system won't let the pilot skid the wheels. Some systems are fully modulating, which means they do all the work. Other systems, particularly on some smaller airplanes, do not fully modulate. They will work to prevent a skid, but aren't pilot proof.
Also part of the anti-skid system are autobrake systems. These apply brakes automatically to achieve a predetermined rate of acceleration (or "deceleration," if you prefer). There are typically several levels or degrees of antiskid, depending on how much braking should be done. Different aircraft and different operators have their own ways of utilizing these systems. With autobrakes, the system only cares how fast the aircraft slows down...not how much brake pressure is applied. If the pilot uses reverse thrust, the brake system won't work so hard, won't heat up so much, and won't use as much brake energy to slow the aircraft...but it will still slow at the predetermined rate...the slowing effect being a combination of braking and other inputs such as the reverse thrust. In the maximum setting, full braking energy is used, just shy of skidding the wheels, and any outside decelerating force such as reverse thrust is added to the braking effect, or increases the rate at which the aircraft slows down. Autobrakes are a part of the anti-skid system, and are used for landing.
Another feature many aircraft use are takeoff autobrakes, sometimes called RTO brakes (rejected takeoff brakes). These are also part of the antiskid system, and serve in a similiar fashion to the landing autobrakes. Braking is automatically applied if a takeoff is rejected. Various parameters arm them: a certain amount of power lever travel, a certain velocity (80 knots, for example) on certain sets of wheels, etc, tell the system the aircraft is taking off. If other triggers occur, such as retarding certain power levers, the takeoff autobrakes kick into effect, and apply maximum braking to the aircraft.
Some systems use the brake valves to accomplish automatic braking, some use a separate system to do this, and each modulates the autobraking using the antiskid system.
Antiskid on an aircraft works very much like antiskid on a car.