In diamond, each carbon atom forms 4 strong covalent sigma bonds with other carbons, resulting in a tetrahedral 3D arrangement of atoms where all the electrons are fixed in place or localised. In graphite, each carbon forms 3 strong covalent sigma bonds with other carbons, resulting in lots of 2D layers with a hexagonal (or trigonal planar) arrangement of carbon atoms and weak forces of interaction between the two layers. As each carbon only forms 3 bonds, only 3 of the 4 outer shell electrons are fixed in place, which means one of the electrons from each carbon is delocalised. These delocalised electrons are free to move around and create a current, which is why graphite conducts electricity and diamond does not.