The ABS pump is part of the Antilock Braking System (ABS). The pump provides pressure to the brakes. After the ABS ECU has detected wheel slip it signals for the valves to open to release the brake, the pump restores braking pressure once the valve closes. It is an integral part of the system and is controlled by the ECU.
Failing ABS pumps can have different symptoms. Generally if you notice changes in the response of the braking pedal there could be an issue with the pump.