When a uranium atom falls apart, it produces energy, some fragments and some free neutron. When a neutron hits another uranium atom, that one falls apart, too. So, the more atoms fall apart, the more neutrons you have flying around and even more atoms fall apart. Obviously, too much is not good, so you use other stuff that can catch neutrons without falling apart and insert that stuff between your uranium fuel rods. Those are the control rods. With them, you make sure that just the right amount of uranium falls apart.
The energy that is released by the falling apart of the uranium turns water into steam, and that runs a turbine and a generator, just like in a coal plant.
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