There are different kinds of conductors, most notably electrical and thermal conductors. But they are often inclusive of each other (electrical conductors are typically good thermal conductors).
A conductor transmits something through its body with high efficiency while an insulator does not transmit very well. In the case of electricity, a conductor transmits electrical energy between two points while an insulator blocks the flow of electricity.
Two examples of conductors are copper and silver. Two examples of insulators are wood and styrofoam.