Computer chips use a lot of power in the relatively small wafer area of the computer chip. The computer chip, CPU, offers resistance to that power as it does its work. The result of that amount of power with that much resistance is heat. The same thing happens with a light bulb. You push a lot of power through the filament to produce light, and the result of this is a lot of heat or a very hot light bulb.
The faster the computer chip, the hotter the computer chip. The heat if it gets too hot can start causing problems in the operation of the chip and the motherboard. The way around this is to use a heat sink with a fan placed directly in contact with the computer chip to dissipate the heat. Thus we have the CPU cooling fan. All current computer chips require a CPU cooling fan.
There's a couple of ways to go. When you order a cpu, it comes with a fan. You're all set. However, most computer enthusiast don't think those fans are good enough, and want to order a better fan for their computer for a number of reasons: they anticipate overclocking the cpu, producing more than normal heat; they want a super quiet fan, as the packaged fan usually is noisy; you want your rig to look good, you can get lights with your fan.
If you would like to order a CPU cooling fan. There are some things to consider: The first is noise. CPU fans can be noisy. You can replace the CPU fan with a less noisy fan. Look on the CPU Cooling Fan specification for the Noise Level. The lower the dba the better.
Cooper heat sinks exchange heat better than aluminum.
CPU fans/heat sinks are made for certain computer chips and sockets. If you order a Intel Core 2 Duo, which has an LGA 775 socket, you need to order a fan made for that socket and chip.
CPU fans attach in two ways. There are four holes through the mother board around the chip socket. The heat sink of tha fan sits on top of the computer chip. The fan body either has four push pins that push into those four holes in the motherboard and are held firmly in the holes by expanding the pin after it is through the hole. Or you screw the fan into a plate on the underside of the board. I've found the push pin types are flimsy and the pins break easily. I prefer the type where you screw into a plate on the back of the motherboard. "Zalman" is a brand name that uses this technique.
One other thing you'll need is thermal grease. This is a grease mixture that you place between the CPU chip and the heat sink to enhance the heat transfer. I recommend a brand called "Arctic Silver." It comes in a tube with an applicator for about $7.