Disclaimer: I haven't operated a nuclear reactor since 1984 and I have not kept up with it closely. But I do know some basics and have written a short note. I warmly welcome correction or elaboration from those who know more.
The Fukushima nuclear power station has 6 so-called "boiling water reactors"
In these type of reactors, water is sent through the core, boils and turns into steam which in turn spins the blades of a power generating turbine. The steam is then condensed back into water and goes through the core again. This steam/water is radioactive.
The reactors have been shut down; the control rods (which absorb neutrons which cause the fissions) are down. But, a significant amount of heat comes from the radioactive decay of the fission products; this is called "decay heat":
when a uranium atom splits, there are two new atoms formed. These atoms are unstable and will decay and release gamma radiation (very strong rays caused by a change of energy states; these similar to x-rays but stronger). This gamma decay generates a significant amount of heat; depending on reactor design this can account for more than 10 percent of a reactors power. I don't know what percentage of power that decay heat accounts for in the Fukushima design.
Hence the core has to be cooled even if the reactor has been shut down; heat is still being generated and the core has to remain covered.
We have radioactive steam problems (hence the pressure build up), escape of gasses in the water, and of course, some potential for the overheated fuel pellets to melt.
I do not know what the odds are in this situation.
This will NOT be a Chernobyl situation as there was a graphite fire in Chernobyl and this reactor has no graphite; also Chernobyl didn't have a containment building. This is more similar to the Three Mile Island situation.
Bottom line: they need to get some water circulation in the primary system (the water system that runs through the core) to keep the core cool.
The explosion: could have been many things, including many non-nuclear things.