Disclosure: I work in the field of computational biology and protein folding
Folding@home is a framework for distributed computing, started and maintained by Vijay Pande at Stanford. There are several similar distributed computing projects like Rosetta@home and Seti@home ...they all exist because the researchers have a need to do computationally expensive calculations.
There are two ways to process computationally demanding jobs: 1) use a single super-computer that has many CPU's and memory structures in parallel, 2) use many individual CPU's, and distribute the work load accordingly. Some jobs are easily parallelizable...that is, it is easy to cut the one big job up into many useful smaller parts, and then recombine the results at the end. Other jobs are not easily parallelizable...usually because the job is such that results from one calculation depend on the state of another calculation (ie, the calculation is highly coupled).
The goal of Folding@home and Rosetta@home is to test methods for folding proteins, computationally. The protein folding problem is one of the major challenges in biology and chemistry today; these folks are trying to develop methods to predict the 3D structure of proteins, given a 1D sequence of amino acids. It is a hard problem that can be broken down into 2 challenges: search and scoring. The second challenge is mostly addressed by the really bright researchers working in groups such as Pande's and Baker's (and many more, this is a huge worldwide effort). The first problem has (so far) been tackled most successfully by using super-computers such as the Blue Gene and distributed schemes such as Rosetta@home.
Thus, using your spare CPU cycles, Vijay Pande et al. are leveraging many small increments of CPU power to have a parallel super-computer of sorts. "Donating" your CPU cycles therefore enables the problem of protein folding to be tackled by some of the brightest in the field. Thanks!
Also, I find it interesting that PS3's (Playstation 3's) account for ~90% of the processing units on the Folding@home network now. Yay, Cell processors!
