That would be a good question over at the Uranium room but since it has not been populated yet, here is the gist: The core of an atom (i.e. its nucleus) is provided with an additional particle (a neutron), which causes the atom to break up in smaller pieces, thereby releasing heat that generates steam, from which turbines can generate electricity.
An example would be the reaction of Uranium-235 with a neutron, turning it into Uranium-236 that is unstable and breaks up (236=141+92+3) into Barium-141 and Krypton-92 plus three neutrons that can be used to help break up other Uranium-235 atoms in what is called a chain reaction.
There are two types of nuclear power, fission and fusion.
Fission is where atoms are ‘split’ by bombarding them with other particles. This causes a huge released of stored energy from within the atom itself. This energy is used to create electricity, or make bombs of course. It does not produce greenhouse gases but the waste is radioactive. This type of power is what is found in a nuclear power station.
Fusion is the nuclear power that keeps the sun going but as yet we have not managed to use it to create electricity because it is so hot. Hydrogen bombs use this type of nuclear energy. Nuclear fusion is the opposite of nuclear fission as atoms are smashed together to make larger atoms and this reaction releases energy.