Basically, Stanford University sends out little projects (Work Units/WU) to your computer. Your CPU or GPU then completes the project, and sends the results back to Stanford. Each WU has a different value, depending on the difficulty and the method (CPU/GPU).
The reason? Proteins. I'm not going to go into any biology (partly because I don't like it or understand it), but just accept that proteins fold, similar to a piece of paper. Now, sometimes these proteins can fold unnaturally ("misfold"). This can lead to many diseases like Huntington's, Alzheimer's and some forms of cancer.
The WUs are each projects on how these proteins misfold, and under what circumstances. By getting this information from us, Stanford is able to better understand why the proteins misfold, in the hope that they may eventually find a cure, or at least slow down the disease.
The term used is "distributed computing". What this is, is instead of Stanford spending millions of dollars to fund a massive supercomputer, they send out WUs to us, so we can do the work. In return, they give us points for each WU. It's meant to give a sense of competition about it all, since we all love a good rivalry.
That's about it for the background. Now if you want to get started, take a look at this thread. It has links for all the guides you'll need. Take a look in particular at GPU (the fastest type of folding; however, better with nVidia cards than ATI for the time being), SMP (for CPU folding. Slower than GPU, but still worth having if the computer is being left on) and Fahmon (for monitoring your folding).
If you need any more help, just ask.