A caul is a historical headress worn by women that covers tied-up hair. A fancy caul could be made of satin

Satin

Satin is a weave that typically has a glossy surface and a dull back. It is a warp-dominated weaving technique that forms a minimum number of interlacings in a fabric. If a fabric is formed with a satin weave using filament fibres such as silk, nylon, or polyester, the corresponding fabric is...

, 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:...

, fine silk

Silk

Silk is a natural protein fiber, some forms of which can be woven into textiles. The best-known type of silk is obtained from the cocoons of the larvae of the mulberry silkworm Bombyx mori reared in captivity...

 or brocade

Brocade

Brocade is a class of richly decorative shuttle-woven fabrics, often made in colored silks and with or without gold and silver threads. The name, related to the same root as the word "broccoli," comes from Italian broccato meaning "embossed cloth," originally past participle of the verb broccare...

, although a simple caul would commonly be made of white linen

Linen

Linen is a textile made from the fibers of the flax plant, Linum usitatissimum. Linen is labor-intensive to manufacture, but when it is made into garments, it is valued for its exceptional coolness and freshness in hot weather....

 or cotton

Cotton

Cotton is a soft, fluffy staple fiber that grows in a boll, or protective capsule, around the seeds of cotton plants of the genus Gossypium. The fiber is almost pure cellulose. The botanical purpose of cotton fiber is to aid in seed dispersal....

. The caul could be covered by a crespine or a mesh net to secure it from falling off.
It is also the name of an Elizabethan hair net.