ABS works by detecting individual wheel-lock and momentarily releasing the brakes on that wheel, by decreasing the amount of brake fluid supplied to the wheel to allow the wheel to regain traction.
ABS prevents wheel lock-up and consequent sliding under heavy braking or on slippery road surfaces. Wheel lock-up causes loss of steering and vehicle control, so ABS allows the driver to steer away from hazards, even on slippery surfaces, while applying maximum braking force.
Short and explanatory. Nice one.