The purpose of the air pump is to add more oxygen to the exhaust during cold enrichment to facilitate faster warmup of the catalyst thus the system goes into closed loop sooner. The air pump is also used by the computer to test the Oxygen sensor.
The most common failure is the double bearing in the pulley. Pulley kits are available on line #104 140 02 86 (they're not cheap) or take a chance with a used part.
Mike