When the reactor is shut down it's no longer generating power. Specifically, when the control rods have been "scram"ed there is no longer enough power being produced by the reactor to turn the turbines and their generators.

However, the shutdown nuclear reactor still requires power to maintain proper cooling. The reactor core itself is at an incredibly high temperature and it continues to generate heat as the fission byproducts undergo radioactive decay. Generally only active cooling is sufficient to maintain a sufficient rate of cooling for used reactor fuel, that requires a continuous flow of coolant which requires a power source.

Very simply, when a nuclear reactor stops, the fission products in the fuel rods continue to decay and therefore continue to generate heat. A lot of heat. An external power source is needed to take that heat away from the fuel. Failing to keep the reactor cool can potentially be rather catastrophic.

There is lots of information online. Why not start here:

http://en.wikipedia.org/wiki/Nuclear_safety#Failure_modes_of...

Because when it's shut down, it's not making power anymore...

(It needs power even when operating, but that's for regulatory reasons to maintain redundancy, if I understand correctly.)