Graphite is an allotrope (a different structural form) of carbon (so is diamond), but unlike diamond, graphite can conduct electricity. The reason is that graphite consists of flat hexagons, all liked together in a flat plane. The carbons in the hexagons have delocalized pi bonding (pi bonds, along with a sigma bond, make up a double bond) which allows electrons to easily move from atom to atom, and that is the definition of conductivity.
"good conductor" is not a material classification. "Good conductor" just means its conductivity is interestingly high compared to other materials.
"Semiconductor" specifically refers to materials that are in the in-between of full conductors and insulators. And semiconductor specifically refers to materials that have the band-gap phenomena of electric current conduction.
And personally, I wouldn't consider graphite that good of a conductor. Cast iron is about 340 times better than graphite...yet you don't see us building cast iron wires yet.
