Inside every nuclear reactor, energy is released by the splitting (fissioning) of certain very special kinds of atoms, called "fissile" atoms; these fissile atoms are either uranium atoms or plutonium atoms.
When a fissile atom is struck by a tiny subatomic projectile called a neutron, the atom breaks into two unequal "chunks" called "fission products", and a lot of heat energy is released. That heat is used to boil water, and the resulting steam is used to turn a turbine and generate electricity.
By controlling the number of neutrons that are available, the fission process can be speeded up, slowed down, or stopped. When neutron absorbing material is inserted into the core area of the reactor, neutrons are sopped up like a sponge sops up water, and the fission process slows down or grinds to a halt because there aren't enough neutrons left to keep the chain reaction going. Conversely, removing the neutron absorbing material allows the chain reaction to resume or to accelerate.
But even if a reactor is completely shut down, so that all the fissioning of atoms is stopped, there is still a tremendous amount of heat being generated by the radioactive disintegration of the fission products. This residual heat generation, called "decay heat", cannot be stopped because it is due entirely to the radioactivity of the fission products - and nobody knows how to shut off radioactivity.
The fission products are highly radioactive - millions of times more radioactive than the fissile atoms from which they were formed. And there is a bewildering variety of fission products, including such dangerous materials as iodine-131, cesium-137, strontium-90, krypton-85, and xenon-133, which can be released into the atmosphere as gases or vapours if the fuel is damaged in any way.
Radioactive releases become greater as the temperature climbs, driven by the decay heat. When the fuel melts at a temperature of 1800 degrees Celsius, the amount of radioactive material given off into the environment can be catastrophic, causing many thousands of deaths and contaminating large areas of land so they can no longer be used for habitation or cultivation.
To make matters worse, when water is added to the over-heated fuel, it is possible that the necessary neutron absorbing material is compromised or insufficient and the nuclear fission reaction can begin again, all by itself. This is called "accidental criticality".
When accidental criticality occurs, there is an additional surge of heat and more fission products are created as well, making the situation all the more dangerous. More heat means more melting and more radioactive releases. More fission products means there is more to be released.