Graphite is soft solid lubricant extremely difficult to melt. The reason for this anomalous behavior is that graphite:
In graphite, carbon is sp2 hybridized and each carbon is thus linked to three other carbon atoms forming hexagonal rings. Since only three electrons of each carbon are used in making a hexagonal ring, the fourth electron of each carbon is free to move and is thus delocalized ober the ring. This makes graphite good conductors of electricity.
Also, graphite has a two-dimensional shell-like structure. Such sheets are held together by weak van der Waals forces; it is because of these weak forces of attraction, one layer can slip over the other thus graphite acts as an exceptional lubricant.