Why does metal conduct heat well?
Poor electrical conductors like glass, plastic, wood, etc. conduct heat mainly through vibrations among the molecules. As molecules vibrate, they bump into their neighbors from time to time, transferring some of their energy (i.e. heat). Those neighbors then bump in to some of their neighbors on the other side and transfer some of the energy to them. The process continues, and the heat is transferred through the material, but it happens quite slowly because the molecules are mostly stuck in place (because they're part of a solid material. If they were liquid or gas, they could move around more freely and transport heat more quickly. That process is called convection, rather than conduction).
Anyway, metals and other good electrical conductors have the ability to transfer energy through an additional mechanism. In this case, the vibrating molecules literally shake off some of their weakly-bound electrons (which are plentiful in metals and all other good electrical conductors). These high-energy electrons then fly away and bump into other molecules or electrons, transferring the heat. Unlike entire vibrating molecules, however, individual electrons are so small that they can travel much longer distances at much, much higher speeds before they bump into anything. (It's sort of like shooting a gun in a forest. The bullet may travel several hundred feet or more before it actually strikes a tree. If you tried to drive a bus in that same forest, however, you couldn't go more than a few feet without running into something).