Definition: Graphite is a form of carbon which is an element. In graphite, the carbon atoms are joined together and arranged in layers. The links between the carbon atoms in the layer are strong, but the links between the layers are weak. The layers easily slip over each other. That's why graphite in a pencil is soft and you can see a mark when you write with it on paper.
Graphite is a non-metal and it is the only non-metal that can conduct electricity. You can find non-metals on the right side of the periodic table and graphite is the only non-metal that is a good conductor of electricity.