The operation of a nuclear power plant depends solely on 2 main elements, the nuclear reactionsin the nuclear reactor, and the power generation process by the steam turbine.
The nuclear reactor creates a condusive envorinment for the nuclear fission reactions of the fuel to occur. This reaction generates extensive amounts of heat energy which will then be the converted to electrical energy by means of a steam power cycle.
The steam power cycle used in a nuclear power plant is similiar to that in a steam power plant, where the heat source is used to heat the water into steam or superheated steam, and then directed to the turbines to generate electricity. The steam or sometimes water that leaves the turbine has a lower temperature as compared to when it
first entered the turbine. It is then pumped back into the reactor containment structure where it absorb the heat generated from the reactor core once again, and the whole process repeats itself.
With that said, there are 2 types of nuclear reactor types, the Pressurized Water Reactor (PWR), and the Boiling Water Reactor (BWR). The difference between these 2 is that in a PWR, the heated water is pressurized to very high pressures (the water does not boil due to high pressures) before it enters the turbine generators. Whereas in the BWR, the water is just heated until boiling point temperature, turning into steam just before it enters the turbine generator.

Regardless of the type of reactor, nuclear power plants generally have very high power generation rates due to the massive amount of energy released from nuclear fission reactions. From this, it also could be said that nuclear power plants also have very dense energy generation, meaning that one nuclear plant generates far more electrical power than a conventional coal power plant.
Nuclear power plants also have virtually ZERO emmisions of green house gasees. The fuel (uranium) is also currently inexpensive and easily attainable, and not to mention the volumes of nuclear waste produced are significantly lesser than the wastes from coal burning. Considering all these advantages, it is no wonder why nuclear energy is taken into serious consideration as an alternate energy source.