The ABS control module (also known as antilock braking system) is basically a microprocessor which runs the diagnostic checks of a car. In addition, it helps to process information from the hydraulic brake system as well as wheel-speed sensors to measure when is the right time to release the braking pressure on a wheel, which is going to lock up and begin skidding. In other words, antilock system would prevent skids when you are braking, and stability control intervene to avoid skids even when the brakes are not used.
In general, an ABS warning light on the dash is often supposed to be on for a couple seconds each time a car is started. However, if it is on when you are driving, that would be a signal that the wheel sensors have failed, the control modules have conked out or another issue has just developed.