It's a boiling water type reactor. A steel pressurized reactor vessel (which is inside the containment building) holds the fuel rods, control rods, etc. The control rods are below the fuel rods, so in theory if the fuel rods do melt, then they melt down into the control rods which slow (but won't completely stop) the reaction.
Water circulates around the fuel rods, and this water is inside the pressure vessel and circulation system, and is not allowed to escape, to avoid radiation leakage. However, if this water is pressurized too high, then the pressure vessel and circulation system could explode.
Yesterday they released some of this water into the atmosphere as steam to prevent a much larger explosion that would result if they didn't relieve the pressure. It is this steam that has caused the radiation detectors, and a few people, to test as radioactive, and it's why that radiation has fallen back down - they relieved the pressure and stopped releasing the steam once the pressure was within safe limits. The radiation that was released was minimal on the scale of things.
I suspect that they started pumping sea water directly on the pressure vessel inside the containment building, and that they didn't have adequate means of draining the building, let alone enough venting so the pressure inside the containment building didn't get too high. Once the water hit the reactor, it steamed up, and pressurized the containment building, and eventually it failed.
From the articles, it sounds like radiation has not increased appreciably since the containment building fell, which indicates the pressure vessel is still intact. And, in fact, it should be a lot easier to cool the reactor core from the outside.
As long as they can cool it enough to keep it from melting down too much, and they can get the regular cooling system back online, then things will be fine.
If they can't cool it fast enough for long enough, then a meltdown will cause a large-scale environmental disaster, however it is unlikely that it would be as bad as chernobyl. Not only did Chernobyl NOT have a containment building to start out with, they did not bleed off the excess pressure inside the pressure vessel quickly enough, and it exploded, sending all sorts of radioactive material into the air. As long as they release the pressure at this plant as needed, and keep pumping cool water in to replace the water lost as steam, then they should be able to prevent an explosion, and even if radioactive steam is released it will be significantly less radioactive than a pressure vessel breach.
The fact that they blew up the containment building indicates that either someone made a really bad mistake (not just a poor choice) or that the situation is so bad that they are pulling out all the stops. The "dust" from the "explosion" is more likely to be the huge amount of steam that was contained in the building before it failed, along with some real dust and debris. It's not a small thing, though. In the US the containment building itself, by regulation, must be able to withstand the impact of a fully loaded passenger jet without breach.
The pressure vessel has concrete walls that are measured in meters of concrete and steel thick. If it does go into full meltdown, and they can't control the heat, then the explosion that results will be astonishing, and radiation detectors worldwide would be going off, depending on the air currents. The fuel will be liquid by that time, which will make it easier to disperse aerially. The fuel load of these reactors is in the area of 150 tons of Uranium, which is about a speck of uranium per person on the planet.
Unfortunately that thick concrete and steel pressure vessel also makes it harder to effectively cool it from the outside, so they have to get the regular cooling system online as quickly as possible.
http://en.wikipedia.org/wiki/Fukushima_I_Nuclear_Power_Plant
http://en.wikipedia.org/wiki/Boiling_Water_Reactor