It's a project to figure out how proteins folds themselves, they run simulations of folding proteins on every computer running Folding@home. So your computer could donate its spare CPU/GPU time to research.

So do they use your computer remotely?

No, nothing of the sort.  They send your computer problems that would normally take a lot of power to do together, but have been reduced and sent to your computer.  For example, they may not ask to fold an entire protein, but only a very very small part of it.  They send your computer work, your computer does it, and returns the output.  It should be safe, and I can pretty much guarantee transactions with folding@home are going to be encrypted in some way if they are important.  Its fine, and safe to use if you want to try it.

Hmm... A little off-topic, but isn't there some college who is doing tests to analyze data collected from space and who is using some kind of method like this? Where you download a program, and it receives data, works on it, then sends it back?

Yes, most likely SETI, which is done by berkeley, I believe.  I don't remember, because BOINC is what most of the @home projects use, and it is good for distributed computing, and it is also done by berkeley.