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But basically, it's a project to discover how proteins fold with a view to finding cures for diseases and stuff. The project is split up in to little chunks and distributed out to people al over the internet who run the client program on their machines who process the data and return the results. Those people are credited with points for the units they return, and are generally part of a team which leads to a bit of friendly competition.
Yeah the standford folding website as posted by Forthy is the best place to get lots of information about folding@home. But basically the project uses idle cpu cycles (it runs in the backround and doesn't slow down your computer because it gives priority to any other program) to study protein folding, a natural process that happens whenever cells divide. Protein folding is very complicated, and it is hard to prove theories about how it might work, so this project is designed to create a computer simulation of the process to make it easy to study.
When proteins misfold, they can cause many diseases, so understanding protein folding is sort of like the "holy grail" of molecular biology.
With folding, it doesn't have to cost you anything, and you could help save many lives in the future. That's why it's so popular. If you want to now why so many members of this and other teams spend so much money and time trying to help the project as much as possible, just read the sticky "Why we DC" at the top of the forum.