Denier is a method for measuring the fineness of fibers commonly used in the United States The definition is rather complicated. It is defined as the mass in grams of one strand of fiber 9000 meters long. Thus if we say a fiber is 3 denier or 3d, one strand of that fiber 9000 meters long weighs 3 grams. Fibers of low denier are soft and silky and those of high denier are coarse like steel wool.
The metric system measure of the fineness of fiber is dtex. Dtex is the mass in grams of one strand of fiber 10,000 meters long. The dtex measurement will always be a little higher than the denier for the same strand of fiber.
The photographs below are all at 60X magnification.