What is it about the structure and bonding of graphite that allows it to conduct electricity?

Graphite has a giant covalent structure consisting of layers of carbon atoms. Carbon atoms have 4 valence electrons that are available for bonding. In graphite, each carbon atom is covalently bonded to 3 other carbon atoms. Therefore, every carbon atom has 1 electron that is not used for bonding. These extra electrons are delocalised, or free to move, in the area between layers of carbon atoms. As these electrons are free to move they are able to carry charge and thus graphite can conduct electricity.