I will try and keep this simple, but the bottom line is that the danger you are hearing on the constant news is overblown.
First, the reactors that are considered in danger are all shut down, the control rods are in the core. The only concern is decay heat, which represents 3% of the operating power, and it is reduced exponentially every day that passes.
Second, reactors have three levels of primary protection: the fuel cladding (the metal casing that holds the fuel together), the reactor vessel (4-8" thick metal containment vessel), and the primary containment (40-80 inch thick concrete and steel building). So far, only the fuel cladding has been compromised (some cladding "meltdown" experienced), and that is why there is not a significant release of radiation (clad melts at about 2000 degrees, the fuel itself at 4000 degrees). The pumping of seawater into the containment reduces the potential for the higher temperatures to be realized.
The hydrogen explosions have been due to the release of pressurized gases from the reactor vessel and primary containment, as developed through emergency operating procedures, into the secondary containment. The release of the disassociated hydrogen into the atmosphere, through pinch points, results in gaseous explosion, but not damage to the second or third level of containment protection.
Below are news release details:
The hydrogen explosion on March 11 between the primary containment vessel and secondary containment building of the reactor did not damage the primary containment vessel or the reactor core. To control the pressure of the reactor core, Tokyo Electric Power Co. began to inject seawater and boric acid into the primary containment vessels of Unit 1 on March 12 and Unit 3 on March 13. There is likely some damage to the fuel rods contained in Units 1 and 3.
At both Units 1 and 3, seawater and boric acid is being injected into the reactor using fire pumps. On Unit 3, a pressure relief valve in the containment structure failed to open, but was restored by connecting an air pressure to the line driving valve operation.
The water level in the reactor vessel of Unit 2 is steady (update, seawater injection also required for Unit 2).
Personnel from TEPCO are closely monitoring the status of all three reactors.
The highest recorded radiation level at the Fukushima Daiichi site was 155.7 millirem at 1:52 p.m. EDT on March 13. Radiation levels were reduced to 4.4 millirem by the evening of March 13. The Nuclear Regulatory Commission’s radiation dose limit for the public is 100 millirem per year.
Japanese government officials acknowledged the potential for partial fuel meltdowns at Fukushima Daiichi Units 1 and 3 reactors, but there is no danger for core explosion, as occurred at the nuclear power station at Chernobyl in 1986. Control rods have been successfully inserted at all of the reactors, thereby ending the chain reaction. The reactor cores at Fukushima Daiichi and Daini power stations are surrounded by steel and concrete containment vessels of 40 to 80 inches thick that are designed to contain radioactive materials.