It is the "secondary air pump"
It runs for about 30 seconds on initial start to warm up the Catalytic converters.
It is driven by a relay in the RCM module that is very prone to burning it's contacts and at times welding them together and causing that pump to run until it burns itself out.

If the pump IS burned out, the only effect will probably be annoying P codes and CEL's, the car will run OK.