In many ways a nuclear power plant is just like any regular coal-powered, electricity producing plant. Both turn water into hot steam that turns the turbines connected to an electricity generator which then generates electricity to the grid.
The same water circulates in the plant, in turn as steam and as liquid.
What differentiates a nuclear power plant from a coal plant is the source of the heat. Instead of combustion, water is boiled by the energy of atom-level splitting reaction, i.e. nuclear fission.
In nuclear fission the fuel atom splits into two which releases a large amount of heat. Fissions occur in a chain reaction so that one atom splitting will on average make one new atom split. This is how heat power can be produced evenly.
All the heat in the steam cannot be utilised in heat production, so a part of it must be transferred out of the plant. In Finland, the heat is transferred to the sea with the help of cooling water.
Cooling water is pumped from the sea and then pumped back about 10 degrees warmer. Cooling water is never in contact with the water heated in the reactor, and runs through its own set of pipes. It is not in any point in any contact with anything radioactive.
Most nuclear reactors in the world are light water reactors: regular water passes through them to cool the fuel and to sustain the chain reaction.
In other reactor types, the reactor can be cooled, for example, by using helium gas or the chain reaction can be sustained using graphite.
Light water reactors can be further divided into pressurised and boiling water reactors. They are equally common, and in Finland there are two of each in use. With respect to safety, pressure and boiling water reactors do not have any essential differences.
As the name indicates, in boiling water reactors the water boils in the reactor around the fuel. The steam generated from this flows directly to the turbine island, and returns to the reactor having gone through the turbines and cooling system to be boiled again.
In a pressurised water reactor, the water that flows through the reactor is at a very high pressure which is why it will not boil even at over 300 degrees. The heat is transferred from the water running through the reactor to another circuit in the steamers, which act as massive heat exchangers. In the second circuit, the water is at a lower pressure, so it boils into steam that turns the turbines.