The spark plug heat range refers to how well the center electrode conducts heat to the head.
A hot plug can't conduct the heat very well that is what makes them hot, they can't cool themselves. A cold plug conducts heat well, by moving heat away quickly the spark plug stays cool.
The need to control the temperature of the center electrode comes from the need to keep the center electrode clean. There are three general temperature ranges. If the temperature of the center electrode is too cool, deposits will build up on the electrode. If the temperature of the center electrode is too high then there is a chance for igniting the air fuel mixture prematurely. If the temperature is just right then the spark plug cleans off the deposits without preignition.
The subject of heat range comes up when performance modifications are made to an engine. It is common for these modifications to increase the combustion temperature. With the increased combustion temperature a colder spark plug is needed to make sure that the center electrode doesn't get too hot and allow preignition does not occur.