Everything is made of tiny things called atoms. All atoms have a tiny center part called the nucleus. Some atoms have an unusual type of nucleus that, every once in a long while, randomly explodes, sending tiny pieces in all directions. Normally those tiny pieces just bounce around until they join another atom. However, if you have a bunch of the right kind of exploding nuclei together, the exploding pieces of one nucleus can hit other exploding nuclei, and make them explode immediately, then those pieces hit even more exploding nuclei, and you get a chain reaction, sort of like dominoes.
To make a nuclear reactor, you dig up a bunch of rocks with the right kind of exploding atoms, and you carefully remove many of the other atoms so the exploding atoms are close enough together to make a chain reaction, then you put them in water*. All the exploding nuclei produce a lot of heat, which boils the water. The steam turns a fan, which spins a magnet, and creates electricity. You have to be very careful that you don't put too many of the pieces with exploding atoms together, or the atoms will explode too fast, and reactor will get too hot.
*If you want to get into more detail, you could explain that the exploding bits are going so fast, that they usually pass right through the other atoms, cartoon-style, unless you have other atoms, like those in water (a moderator), for them to bounce off of and slow down. You could also explain that reactors use "control rods", which are made of atoms that easily absorb the exploding bits, and therefore slow down the chain reaction. So, if they push the control rods further into the reactor, the chain reaction slows down more.
If you want to include more terminology:
Rocks = Uranium ore
Removing all the other atoms = enrichment
Nucleus exploding = nuclear fission
Exploding atoms = radioactive atoms (often Uranium)
Exploding pieces = neutrons (and some other particles)
Fan = turbine