A nuclear meltdown is a term used to describe damage to a nuclear reactor's core. The core of the nuclear reactor is where the radioactive fuel is kept. As the radioactive fuel undergoes fission, heat is released and this has to be removed with an appropriate mechanism using liquid or gas coolants. The heat that is removed is used to operate the engines that produce electricity.
If there is a problem in the cooling mechanism and it is also not possible to stop the nuclear fission reaction, the complete assembly in which the fuel is kept starts to heat up to extremely high temperatures. As a very large amount of heat is released in fission reactions, the melting point of the material comprising the assembly is soon reached and it starts to melt. If the nuclear reactor's core melts it can lead to escape of the highly radioactive nuclear fuel and cause extensive environmental damage.
The earthquake in Japan has led to the cooling system in a few of its nuclear reactors getting damaged, with one nuclear reactor having reached temperatures that could lead to a meltdown unless the steps that are being taken to tackle the situation are successful.