Graphite is structured as layers of carbon atoms arranged in 6 atom planar rings. Each carbon atom forms three bonds to neighbouring atoms meaning that each eatom has an unbonded alectron. This unbonded elctron is delocalised into the ring, so there are 6 delocalised elctrons per ring. These delocalised elctrons are free to carry charge throughout the structure, hence graphite conducts electricity when a potential difference is applied.