When a nuclear power reactor is in normal operation, heat produced in the reactor core is used to produce steam, which runs turbines to generate electricity.
When a nuclear power reactor is shut down, the nuclear fission reactions are stopped, but the radioactive material in the core of a nuclear reactor continues to generate heat long after the nuclear fission reactions have been shut down. This heat must be removed from the reactor core in order to prevent damage to the structure of the reactor, which could then result in the escape of radioactive material.
The heat produced in a dormant nuclear reactor is removed by pumping coolant through the core. Electricity is required to run the coolant pumps. Normally, external electricity would be available from the power grid. In an emergency, on site diesel generators would supply the power needed to run the cooling pumps, and battery power would be available only for a short time until the diesel generators could be started.
At the Fukushima Dai-ichi Nuclear Power Station, the reactors were shut down, and core cooling started, but then the tsunami struck, off site power was lost, and the switch rooms and diesel generators were flooded and damaged. There was no power available to run the core cooling. Desperate attempts were made using fire trucks pumping sea water to cool the reactors.
As temperature in a reactor core increased, the water in the reactor core began to boil, producing steam, increasing the pressure in the reactor vessel. The steam had to be vented in order to prevent the reactor vessel from bursting, and releasing its dangerous radioactive contents.
From reports, it seems that enough water in the reactor core had boiled away to leave fuel rods exposed above the level of the water. These became so hot, that they burned, taking oxygen from the steam, freeing hydrogen, which was vented with the steam in order to reduce the pressure in the reactor vessel. The hydrogen accumulated in the containment building and eventually exploded, blowing away the roof and walls, leaving the reactor vessel exposed.
The presence of iodine and caesium in the dust following the explosion indicates to me that the vessel containing the reactor core has been damaged, and that radioactive fission products are escaping from damaged fuel rods.
According to reports, hydrogen explosions have damaged the containment buildings of Fukushima Dai-ichi nuclear reactors numbers 1, 2, and 3. Also, the level in the cooling pond for spent fuel rods at reactor number 4 has exposed used fuel rods, causing a fire and releasing radioactive material from the fuel rods.
Particularly worrying is the use of a mixture of plutonium and uranium as fuel for Fukushima Dai-ichi reactor number 3. Plutonium is absorbed in the body as a iron substitute and circulates in the blood irradiating the entire body. (See also destroyer of DNA for the effects of radioactive iodine, caesium, and strontium)
In order to prevent radioactive contamination of northeastern Japan, each Fukushima Dai-ichi reactor vessel must be entombed in a sarcophagus of sand and concrete. Even this may not be effective if the radioactive material melts through the bottom of a reactor vessel and reaches the water table.