Copper is a good conductor of electricity because the valence electrons are free and repel each other so strongly that it causes the repulsion of other electrons. This essentially forces the electricity down the piece of copper, or conducts it down the metal.
Any external influence will cause the repulsion action, so the force of the electricity itself is what sets the conduction into motion. This repelling movement allows the electricity to move freely, unlike non-metallic solids that are comprised of atoms which hold onto their electrons tightly. That tight bond keeps the electricity from flowing from point A to point B. There are many metals that can be used as a conductor, but copper is one of the most popular.