Why is copper the best heat conductor?

It is not necessarily the best heat conductor, in fact aluminum is a far better heat conductor

Aluminium is not a better thermal conductor than copper, in fact copper's conductivity is about twice that of aluminium. However, Silver is slightly better than copper in this respect, and so is diamond, but these are both expensive to produce and silver corrodes quickly, so copper is often the material of choice for heatsinks, etc. (Pots and pans aren't copper because some copper compounds are harmful, and can transfer taste to food, some pans are made of a steel-copper-steel sandwich)

The above poster is correct in some sense, aluminium is a better conductor per unit weight, rather than per unit volume. In a situation where a light weight is important, aluminium can be used. But if a small volume is important and weight isn't (in a computer), copper is much better suited. (aluminium is cheaper too).

Why is copper better?

Metals conduct heat well for the same reason that they conduct electricity. The electrons are able to move throughout the material and carry the heat energy with them through their kinetic energy, which is then transferred to colder atoms, heating them up further away from the heat source, whereas other materials rely solely on the vibration of atoms passing onto each other, without the free electron effect.

As for why copper is better than other metals, it's past my own knowledge, reasons that I can think of don't check out. As copper is a good electrical conductor also, it's almost certainly to do with the ability of the free electrons to travel through the material, although I'm not sure why they can travel any easier than aluminium.

Hope this helps.