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Why does graphite conduct electricity while diamond does not?

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A color-coded periodic table of the elements displays each element's symbol and atomic number, with categories such as alkali metals, noble gases, halogens, transition metals, and actinoid elements distinguished by different background colors. — carbon group element Modern version of the periodic table of the elements (printable).

The difference in electrical conductivity between diamond and graphite is a direct consequence of their distinct crystal structures.1

In diamond, each carbon atom is covalently bonded to four other carbon atoms in a rigid, three-dimensional tetrahedral lattice. Because all valence electrons are localized in these strong covalent bonds, there are no free electrons available to carry an electrical current, making diamond an electrical insulator.12

In contrast, the structure of graphite consists of parallel layers of carbon atoms arranged in fused hexagonal rings. Within each layer, the carbon atoms exhibit complete $π$ -bonding, which allows for the movement of electrons. This delocalization of electrons within the sheets enables graphite to conduct electricity, particularly in the plane of the layers. The layers themselves are held together by weak van der Waals forces, which do not contribute to the same type of localized bonding found in diamond.12