In diamond each carbon atom is covalently bonded to four other carbon atoms.This arrangement of carbon atoms gives rise to a tetrahedral structure. These small tetrahedrons combine to form a rigid three dimensional network.
In graphite, carbon atoms are bonded together in flat layers by strong covalent bonds in a regularhexagon . These layers are held together by much weaker van der Waals” forces, therefore the crystals of graphite are soft and slippery.