What is a CPU fan?

CPU fan or CPU cooler is only some example of heatsink.
A heatsink is a device that is attached to a microprocessor chip to keep it from overheating by absorbing its heat and dissipating it into the air.
The heatsink may be held in place on the microprocessor by a clip. To ensure that the heatsink can absorb as much heat as possible, thermal grease is used to create a seal between the two devices.
Most heatsinks are aluminum and have fins that extend from the base. An active heatsink is one that comes with a fan, sometimes called a heatsink/fan combo (HSF). A passive heatsink is one that comes without a fan.