The basic idea behind Anti-lock Braking Systems (ABS) comes down to the difference between kinetic friction and static friction. Imagine you're trying to push a heavy box across a floor. You push it as hard as you can, and finally it budges. You notice that keeping the box moving requires much less force than it initially took to get the box to budge. This is the difference between static friction (friction between two objects that aren't moving relative to one another) and kinetic friction (sliding friction). The basic formula for friction force is:
where N is the normal force (basically any forces pushing an object toward the ground- weight, downforce, etc.) and mu is the friction coefficient. Static friction coefficients are larger than coefficients of kinetic friction. When you hit the brakes on your car, you therefore want your vehicles to roll to a stop so as to ensure that the wheels are slowing down due mostly to static friction (also called rolling friction), not purely kinetic friction (sliding friction). This often maximizes the friction force and can decrease stopping distances, especially on paved surfaces.
A standard Anti-lock Braking System uses four wheel speed sensors, a hydraulic pump, four hydraulic valves (assuming it is a 4 channel setup), and a controller. The controller in the ABS system monitors the speed of each wheel using the wheel speed sensors, which are usually hall effect sensors. If the controller sees that one wheel is decelerating at a rate that couldn't possibly correspond to the vehicle's rate of deceleration, it actuates the hydraulic valve in that wheel's brake line to reduce the brake pressure applied to that wheel. This allows the wheel to turn faster. Once the wheel is back up to speed, it uses the pump to introduce the pressure back into that brake line, applying that brake again. When the controller sees rapid deceleration again, it activates the valve and the cycle repeats about 15 times per second