It is not really called a good conductor but infact it is called a semi-conductor . other non-metals don't have hexagons which allow thier electrons  to move from particle to particle . Moreover as graphite has only one electron but the other NON-METALS  do not have electrons  IN THEM .Graphite and metals have free electrons to conduct electricity. 

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Graphite is a non metal but it is an allotrope of carbon. It has several rows of hexagonal structures attached to each other and are arranged in sheets. Carbon atoms are present at the corners of the hexagons. Because of delocalised pi bonding, the electrons can easily move from one atom to another. Conduction is nothing but movement of electrons which happens very much in graphite. Hence graphite is a good conductor of electricity.
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