What's the purpose of anti-lock braking systems?

I take it you're not a driver. It becomes pretty clear when you are. Basically if you're driving a car without ABS and you have to stop suddenly, the stopping of the wheels provokes a slide because of the weight of the car (kinetic friction). So in order to stop, you have to pump the brake - the initial braking (static friction, if only for a fraction of a second) slows you more than a continuous slide. Pumping the brake slows you much, much more quickly. Stop - slide - stop - slide is better than stop - slide all the way to your target.