It sounds like your chipset fan, what board do you have?
That little fan helps to keep the north bridge chip nice and cool. It's not a good thing that it stopped, but it's not the end of the world either. As long as you have decent airflow through the case and you're not overclocking, it should be OK. But it would be a good idea to either replace it or try giving it a little tune up. In some cases, you can remove the fan and give it a drop of oil to get it going again. There should be a small hole under the sticker on the fan.
Zalman makes a nice little replacement heatsink that works really well: ZALMAN ZM-NB47J Aluminum Heatsink
Overclocking is making the components of your computer such as CPU and video cards, run faster than what they were designed for.
The northbridge chip typically handles communications between the CPU, RAM, AGP or PCI Express, and the southbridge. The southbridge handles things like the IDE (SATA or PATA) controller, USB, ethernet, audio, etc.
Here's a diagram that may help out: