Well in the linked project, the Stanford group uses it to work out how proteins work, in an attempt to understand them and how they go wrong (apparently when they go wrong they can lead to cancer/other diseases).
Essentially the computers of those involved are acting as one large highly distributed supercomputer.
The team element comes from the fact that they give out points for the work units of processing your computers complete (smart really, capitalising on human competitiveness), and a team basically just helps a community show what it is doing.
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