Carbon Fiber - a.k.a. carbon fiber reinforced plastic or carbon fiber composite - is essentially plastic reinforced by a graphic textile. Technically speaking, it is a material consisting of microscopic fibers about 0.0002-0.0004 inches in diameter composed of carbon atoms. It is extremely strong, incredibly light, and very expensive. As such, it's often used in luxury items like high-end planes, boats, bicycles, Formula 1 cars, and here in Michael Toschi shoes and Xikar cigar accessories.
Carbon fiber is prized for its weight-to-stength ratio. When the carbon atoms are bonded with tiny crystals, the resulting fibers are very strong. Yet its density is much lower than that of steel, making it a good fit for applications requiring low weight (i.e. auto racing, flying, cutting a cigar). According to wisegeek.com, "In terms of weight-to-strength ratio, carbon fiber composite is currently the best material that our civilization can produce in appreciable quantities."
For a more in-depth history of Carbon Fiber, its structure and properties, and applications, we'd rather direct you to Wikipedia to read further.