A conductor allows electrons to move freely from particle to particle whereas an insulator does not. This is mainly metals as metallic bonding creates a sea of delocalised electrons that can flow freely. Molten ionic substances also conduct electricity as they have free e- that can move.
just to clarify, there are different kinds of conductors, mainly heat and electricity. A conductor is something that is able to allow heat/elect to flow through it easily whereas insulator, basically means the opposite
