The temperature of a substance is basically a measure of the average kinetic energy of the molecules making up the substance. At room temperature the amount of kinetic energy a molecule has (on average) is about E = nkT/2 where "T" is the temperature and "k" is Boltzmans constant (1.38x10^-23 Joules per degree Kelvin). The variable "n" is the "number of degrees of freedom", which is just an integer that tells us how many ways the molecule can move. For a single atom moving in 3 dimensions (a usual case), n = 3. If an atom moves in 2 dimensions, "n" would be 2 etc. More complicated molecules can rotate and vibrate in addition to just moving in 3 dimensions, so for these "n" can be bigger (5, for example).
Now as you get closer to T=0, the energy falls off more rapidly than that, thanks to quantum effects. Quantum mechanics also tells us that for any system there is generally a lowest possible energy possible, called the "ground state". No-matter what the temperature is, the energy cannot be lower than the ground state energy. Although it seems odd, this is really not inconsistent with the first paragraph. The electron in a hydrogen atom should really NOT be though of as a small particle buzzing around the nucleus like a bee, but rather as a fuzzy cloud centered on the nucleus. The cloud itself can be thought of as motionless, which is a way you can imagine that the atom can have a very low temperature even through the system can not have an energy lower than allowed by its ground state.
Hope that makes a bit of sense.
(republished on 07/25/06)