Graphite forms during the metamorphism, under intense heat and pressure, of coal or limestones with a great deal of organic matter in them. Like diamonds, the other crystalline form of carbon, graphite can be manufactured artificially, but the natural material is still cheaper.
Graphite is widely used in the metal industry for making crucibles that can resist the heat of the foundry. The earliest nuclear reactors had walls of graphite. Nevertheless, under the right conditions, graphite burns. The thick graphite walls of the Chernobyl nuclear reactor caught fire during the catastrophic meltdown of 1986.
Graphite used in pencils has been called "lead" for hundreds of years; in the early days it was thought to be a form of lead metal. In fact, to this day graphite is known in Europe as plumbago, from the Latin word for lead.
The material used in "graphite" tennis racquets is not graphite but a mixture of carbon fibers and resin.
For deeper detail on graphite, including wonderful photos of graphite crystals, visit John Jaszczak's Graphite Page.