When the earthquake hit, the nuclear reactors all automatically shutdown. Within seconds after the earthquake started, the control rods had been inserted into the core and the nuclear chain reaction stopped. At this point, the cooling system has to carry away the residual heat, about 7% of the full power heat load under normal operating conditions.
The earthquake destroyed the external power supply of the nuclear reactor. This is a challenging accident for a nuclear power plant, and is referred to as a "loss of offsite power." The reactor and its backup systems are designed to handle this type of accident by including backup power systems to keep the coolant pumps working. Furthermore, since the power plant had been shut down, it cannot produce any electricity by itself.
For the first hour, the first set of multiple emergency diesel power generators started and provided the electricity that was needed. However, when the tsunami arrived (a very rare and larger than anticipated tsunami) it flooded the diesel generators, causing them to fail.
After they failed the reactor operators switched to emergency battery power. The batteries were designed as one of the backup systems to provide power for cooling the core for 8 hours. And they did.
After 8 hours, the batteries ran out, and the residual heat could not be carried away any more. At this point the plant operators begin to follow emergency procedures that are in place for a "loss of cooling event."
14th EditionR.C. Hibbeler 7th EditionAdel S. Sedra, Kenneth C. Smith 10th EditionR.C. Hibbeler 9th EditionYunus A. Cengel