The basic idea is this:
There is a group who has a project which requires a HUGE amount of processing power and they don't have the money for a supercomputer. They break up the processing into little chunks and distribute it to users who sign up over the internet. The users process their chunk, then return the data to the group who compiles it all together to get something meaningful.
SETI records radio data from the sky and applies a number of algorithms to the signal in hopes of detecting transmissions from another planet. In actuality though this probably won't happen as the aliens would have to be intentionally trying to contact us, or be within something like 20 ly while producing radio "pollution" (like we are) in order for us to find them. This doesn't mean the project is a waste though as it has discovered many new pulsars and other astronomical phenomena, as well as being the DC pioneer.
UD does a number of different projects IIRC. They have a cure for cancer, a smallpox vaccine, and I think a few other projects as well. Your computer simulates proteins folding to create new drugs and whatnot (I'm not very familiar with it though).
Prime95 uses your computer to search for the next highest prime number. This is insanely difficult to do though. I believe the last one found was by a guy on a P200. He started running Prime95 soon after he got his computer new and it took something like 4 years of cpu time to confirm the number he originally downloaded was a prime. Crazy.
It's fun because all DC projects record stats of your performance. <A HREF="http
/setiathome.berkeley.edu/fcgi-bin/fcgi?email=gskamps@interchange.ubc.ca&cmd=user_stats_new" target="_new">Here</A> are my SETI stats, just so you can see what to expect. As you can see, I'm on the THG team so there's that aspect of it too. In the case of Prime95, I know you get a substantial cash prize as well as recognition if your computer discovers a new prime.
Some day I'll be rich and famous for inventing a device that allows you to stab people in the face over the internet.