If a nuclear reactor
is in danger
of overheating, due to a catastrophic loss of coolant
, or withdrawing control rods
all the way, causing critical mass
, the fuel contained within overheats. If the coolant systems and their backup are all working fine, nothing happens, and nothing from here on occurs.
If the reactor gets dangerously close to a meltdown, the reactor can get Scrammed, where it is stopped completely. On a nuclear submarine, seawater is dumped into it to emergency cool it, but it ruins the reactor permanently for the sub (but beware of a Cold Water accident which makes it worse).
The radioactive fuel gets so hot that it begins to melt the container. Once it gets hot enough, it could come in contact with the coolant/water and create an explosion of radioactive steam. That's the first danger, as it could blow the roof off and contaminate the environment for miles around.
Secondly, the core gets so hot it melts together into a slag, and melts/bores its way down into the ground, The China Syndrome.
No nuclear reactor has ever completely melted down, Chernobyl was very close, but didn't completely. It blew the roof and even set the graphite on fire, along with the concrete. It never got to the China Syndrome stage AFAIK.
Three Mile Island had a partial meltdown, but it was contained within the building, keeping the surroundings mostly safe.
If you want to hear a really good account of what goes wrong, step by step, read Tom Clancy's The Hunt for Red October. The same thing almost happened to James Bond in The World is Not Enough