In graphite, each carbon atom is connected to three other atoms and all these bonds lie in one plane, creating a spatial network resembling a honeycomb (carbon atoms connect to form hexagons). Such layers spontaneously stack one above the other, and the distance between them is about two and a half times greater than the length of the carbon-carbon bond. Therefore, these layers are easy to separate from each other. This happens when we use a pencil - each trace of it is exfoliated layers of graphite, and graphene is such an exfoliated layer.
