What you're describing is the 14th century fashion for women to arrange their hair in plaits or braids, sometimes using hair pieces or false hair, which would either be worn in sort of a double column or tube fashion on both sides of the face (which seen, head on, are often mistaken for full "buns"), or in small coiled "horns" (which is usually a slightly later fashion) higher up on the head. Both styles are often termed "cornettes" ("little horns.") The fashion for cornettes ( the tube style) seems to have begun in France and spread outward from there;
it becomes quite ubiquitous in Northern Europe (England, France, the Low Countries, and the Holy Roman Empire) by the middle of the 14th century. In its simplest form (two braids folded in two and held with ribbons) cornettes could be worn by women of a variety of social classes, although they are generally seen on depictions of wealthier women.

We know false hair was used because an extant piece has been found, made of human hair, in London dated to the 14th century. Other references seem to indicate that false hair was sometimes made of flax, wool, cotton, or silk--a bishop in Florence even issued regulations regarding false hair in the early 14th century.

The hair so arranged might be either tied up with ribbons or held in by various types of nets. Fine silk hairnets began to be common in the 13th century, but by the 14th century some of them had started to be made out of thicker stuff, including gold threads and (possibly, if we look at extant statuary and illuminations as a guide) thin, hammered metal strips, sometimes decorated with pearls or other jewels. These nets are usually termed "crespines" or "crispinettes" or sometimes just "cauls". These survived as foundation pieces worn over a variety of braided or coiled hairstyles well into the 16th century. These nets and cauls were luxury items worn by wealthier women.

As mentioned, the more elaborate styles are mostly fashionable evolutions of styles involving plaits or braids that could be worn by women of any class. There was no real "meaning" to the style other than, in the case of the more elaborate examples, as a signifier of wealth and luxury.

Dress Accessories: c. 1150-c. 1450 (Geoff Egan and Frances Prichard) and Textiles and Clothing c. 1150-c.1450 (Crowfoot, Pritchard, and Staniland) both have details of extant finds of the elements of these headdress styles. Stella Mary Newton's Fashion in the Age of the Black Prince contains numerous examples of the use of cornettes.