Short answer: Basically people use their computer at home to contribute to scientific research. You get points for how much your computer contributes. Faster computers score more points. Obviously people here at OCN build fast computers and want to compete with each other. Folding at home provides a way to compete yet do something meaningful with that computer power.
Basically the researchers "borrow" the power of your computer while you are not using it and it does research for them.
I actually work in a computational biology research lab so I can explain it a little. The DNA in your body encodes genes, these genes hold instructions for proteins. Normally the three dimensional structure of a protein is very hard to solve. It takes a year or more of labor intensive work in a professional laboratory. Many proteins are difficult to work with and their structures have not been possible to solve yet. I used to work in a lab that solved these structures. It is horribly slow and laborious.
This is where computational protein simulation or "folding" comes into play. People have been developing programs that can use computers to simulate the structure of a protein. This allows researchers to create realistic models of proteins they otherwise would have no structure of. This can help design drugs and accelerate the progress of disease treatment.
Recently researchers have made it possible for people at home to donate their computers towards running these very "computationally expensive" (as we call it in my lab) programs. Points are given out for how much computation or work a person contributes to the simulation projects.
There are several competing "folding" programs. The folding at home or "F@H" is run out of stanford. This seems to be the most popular here at OCN.
The lab that I work in is a "rosetta" lab. If you are a "BOINC" folder then you are using rosetta more or less.
In my opinion Rosetta (or BOINC) is a much more valid and meaningful use of your computer but F@H seems to have a stranglehold on the popularity.
Most people seem to be more concerned with points and not the science or accuracy behind the simulations. People like to feel they are contributing to science but I feel most of them don't really understand the process and just hope their computer is doing meaningful work. My 2 cents...