Nonian, almost all day-to-day activity in a nuclear power plant is designed to support the plumbing.
The earthquake caused the reactors to shut down automatically. The control rods, which stop the reaction, dropped into the core. The fuel, however, is still very hot. The fuel is in the form of pellets about the size of a pencil eraser and covered with zirconium cladding. They're stacked in long thin fuel rods in a framework and the whole apparatus sits in a large pool of water.
Normally, the circulating water that cools the core after a shutdown is circulated with pumps run by offsite power, but the earthquake took out the transmission lines. When offsite power is cut of off, the emergency generators start automatically, and the six-unit plant had something like 13 generators. However, then the tsunami hit and took those out.
After that, there are two systems that circulate water using convection, and there are batteries. They ran out of battery power and it took a while to get new portable generators to the site. In the meantime, the fuel continued to heat up. If the water boils to the point that the core is uncovered, the cladding on the fuel pellets starts to melt, which releases radioactive particles. Essentially, they had about six backup systems for cooling fail one after the other. At that point, they went to the last ditch step, which is flood the whole containment vessel with seawater and boron.
These are water-moderated reactors, and the water slows down the fission products so that they have a chance to hit each other and cause more fission. Without water, the reaction can't become critical, so you're not talking about an atomic explosion here. However, hydrogen from the melting cladding can (and has) exploded and the steam pressure built up. One or the other has apparent made an opening in the containment vessel at one reactor.
Also, hookers and blow.