The BBC has a pretty decent article on the damage to one of the nuclear powerplants in Japan. The type of reactor involved is a BWR, or boiling-water reactor. The Wikipedia article on these is a bit long, but it operates somewhat like a hot water heater in your house. A nuclear core (2 below) produces heat to boil water (7) into steam (6). That steam is used to spin steam turbines (8 and 9) (like big windmills in theory, but not quite) to produce electricity (10). The steam is then condensed (12) back into water and is sent back into the core (15).
With the earthquake they lost electrical power at the station. This caused the cooling water pumps to stop running. The reactors were automatically shutdown, but because the reactor is full of radioactive material that continues to decay, decay heat continues to heat up the core. They started emergency diesel generators to get those pumps restarted, but those generators apparently cut out shortly after starting. They got temporary generators started eventually for reactors 1 and 2, but not 3.
So, without any cooling, the water left in the core starts to boil off. Think a boiling pot of water. If you put a lid on it, the pressure increases until the lid pops off to relieve that pressure. Reactors have built-in relief valves to relieve this kind of pressure into a containment area. Which appears to be what happened. Here’s where the bad stuff starts. The reactor can get so hot from decay heat that it breaks down the water into hydrogen and oxygen. Well, in this case the hydrogen, oxygen and some spark look to have caused an explosion damaging or destroying the containment (the gray boxes in the above diagrem) for reactor 1, and the fears are it may happen at reactor 3 as well.
This means there may not be a barrier keeping all radioactive material from the reactor from escaping to the environment. The BBC article mentions they’ve detected radioactive cesium. That is potentially very bad. Cesium is a fission product (it is produced by the splitting of uranium fuel atoms) and should be locked up inside the fuel elements inside the core. If we’re detecting it, it might mean that some fuel elements have ruptured. With the possible loss of containment from that hydrogen explosion, we could see the release of some pretty nasty radioactive materials from that reactor.
Now the situation is not hopeless. It sounds like the reactor core and vessel (1) are still intact. The release of radioactive material is most likely from those relief valves I mentioned earlier. So, if you can get the pressure under control so that it doesn’t open the relief valves, you won’t be leaking any radioactive material into the open. The heat produced by the radioactive material in the core decays away exponentially, so as time gone by the situation should get better by itself. Whether that is fast enough to prevent the release of a lot of bad stuff is another story. However, they are apparently flying in spare generators to try and get the cooling pumps running again as well.
So, long story long, this situation is a bit worse than the three-mile island disaster already. It is nowhere near as bad as Chernobyl. I don’t expect things to get much worse at this reactor, but clean-up will be a huge undertaking. Please, ask any questions you might have, and I’ll try to answer them.
EDIT: And as always, it pays to go to the professionals, and not rely on 2nd/3rd hand reports. International Atomic Energy Agency website with updates on Japan.