Diamond structure is tetrahedral, where each carbon atom is bonded tetrahedrally to four other carbon atom. This makes it the hardest natural substance. The bond angles are 109 28'.
Graphite is bonded to three other carbon atoms at an angle of 120 degrees. It is in layers which allows them to slow over each other which is why it is used in pencils. Graphite has a delocalised system of electrons. Because of this it allows graphite to conduct electricity along the layers but not in a direction of a right angle to the layers.