Gemstone facet is a term used to describe a way that a stone is cut. Faceting is done by a Lapidary. A lapidary is a person that cuts small gemstone or woks with gems. Lapidary is not used to denote a person that works with large stones.
It should be noted that faceting is one of four primary ways to cut gemstones or gem materials, the others are tumbling, carving and cabbing. Cabbing refers to making a gemstone in a cabochon shape (spherish shape).
Faceting is the type of cut that is most associated with diamonds. Faceting comes from the term of the different flat surfaces on a diamond or gemstone. Usually the gem or diamond is cut using a faceter. A faceter is a faceting machine. The reason a diamond or any gemstone for that matter is cut using the facet method is to bring out the maximum amount of brilliance and fire of a stone. Brilliance is sometimes called internal luster and it is the reflective quality of light that the gemstone emits, partly due to the gemstones innate qualities and attributes and partly due to the way that it is cut.
While many people might think you need to be an artist to become a good faceter, one ability that is common is the love or grasp of math. Cutting gemstones using the facet method does require math to figure out the best angles to ensure the most brilliance and best showcase of the stone.