An air conditioner pulley uses a belt to spin the compressor, which pressurize the climate system. The pulley is mounted onto the compressor, located on the clutch. When it spins, it is supposed to engage the A/C clutch.
The A/C clutch is a device mounted on top of a compressor, which spins the drive in the compressor. The clutch spins due to the pulley it is connected to, which receives its movement from the belt system on the vehicle.
When the compressor has failed, the belt may squeal, due to the clutch being unable to turn and engage properly, which point will require replacement in order to work.