Primarily, nap is the raised (fuzzy) surface on certain kinds of cloth

Textile

A textile or cloth is a flexible woven material consisting of a network of natural or artificial fibres often referred to as thread or yarn. Yarn is produced by spinning raw fibres of wool, flax, cotton, or other material to produce long strands...

, such as velvet

Velvet

Velvet is a type of woven tufted fabric in which the cut threads are evenly distributed,with a short dense pile, giving it a distinctive feel.The word 'velvety' is used as an adjective to mean -"smooth like velvet".-Composition:...

. Nap can refer additionally to other surfaces that look like the surface of a napped cloth, such as the surface of a felt

Felt

Felt is a non-woven cloth that is produced by matting, condensing and pressing woollen fibres. While some types of felt are very soft, some are tough enough to form construction materials. Felt can be of any colour, and made into any shape or size....

 or beaver hat

Beaver hat

A beaver hat is a hat made from felted beaver fur. They were fashionable across much of Europe during the period 1550-1850 because the soft yet resilient material could be easily combed to make a variety of hat shapes...

.

Starting around the 14th century, the word referred originally to the roughness of woven

Weaving

Weaving is a method of fabric production in which two distinct sets of yarns or threads are interlaced at right angles to form a fabric or cloth. The other methods are knitting, lace making and felting. The longitudinal threads are called the warp and the lateral threads are the weft or filling...

 cloth before it was sheared. When cloth, especially woollen cloth, is woven, the surface of the cloth is not smooth, and this roughness is the nap.