Imagine an anthill, if you are the size of an ant, the hill and the nest that made it is like a city, pretty big! There is a queen ant that co-ordinates all the workers, but they all also act independently, by collective effort large amounts of earth can be moved and structures built, by tiny ants.

BOINC allows someone to create a project like the queen in the ant-hill does, this co-ordinator breaks a big computational problem into ant sized parts, and sends them out to individuals to be completed and returned. With enough ants, its amazing how much research can be completed. Because the ants volunteer their computing power, it makes BOINC a very cheap for scientific problems, that could not normally be funded.