plugged into motherboard
A heatsink is a piece of metal that sits on top of your computers CPU (and also some other components) that helps conduct heat away from it, the fan you're referring to sits on top of the heat sink and moves the heat away and (ideally) out of the case.
Not sure what you mean. The fan is very small and spins to blow air across a heat sink that is attached to the processor. It isn't attached to anything but itself and the housing that screws to the motherboard or case.
The combination heat sink and cooling fan is sometimes called a cooler.
YOu can damage the motherboard
sink
Fan and Heat Sink
I think you mean to ask "what's the function of a heat-sink on a pc motherboard" in which case the function is to keep the cpu cool and prevent it from overheating.
Processor, RAM, daughter cards, CMOS, Heat sink
The heat sink absorbs the heat from the processor and then the fan disperses the heat.
By placing an appropriately sized heat sink and fan on them.
fan and heatsink
It's called a Heat Sink.