What is the reason behind the electrical and thermal conductivity of graphite?

Graphite is a soft, slippery and black material which is an allotrope of carbon.

Each carbon atom in graphite is directly linked to only three carbon atoms through covalent bonds. Therefore, of the four valence electrons in a carbon atom only three are used for bonding and the fourth is relatively free and can pass the electrical current in between the layers. (or this delocalized electrons can move from one carbon atom to the other.) This free electron in the molecule results in the thermal and electrical conductivity of graphite.