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. Generally, a microprocessor's temperature should not run in excess of 50-55 degrees Celsius while under a full load. In Intel computers, the heatsink is positioned either on top of the microprocessor (in computers with a ZIF socket) or on the side of it (in later Pentiums in which the microprocessor fits into a Slot 1 interface). 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.
When you buy a computer or a separate microprocessor, the heatsink comes with it. 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.