If the hydrogen atoms are stripped from a benzene molecule (converting it to a "phenyl group") this unit can be repeatedly bonded together into sheets of "graphene."
The bonding is the same: The first three carbon bonding electrons are tied up in sigma sp2 bonds within the plane. The fourth electron is in a pi configuration perpendicular to the plane. Pi elections on paired carbon atoms then link together to form pi bonds. And as those pairings rapidly change, a continuous moving cloud of pi electrons forms above and below the graphene plane. This movement of pi electrons means that graphene can conduct electrical current.