The wimple - the head veil with the chin covering - was traditional in the Middle Ages for married women. Just like women in Islam today, in certain periods married Christian women were required for religious and modesty reasons to cover their hair.

The cloth that covers the chin was called a barbette, and had the extra benefit of hiding a sagging neck!

I call it a barbette because it appears to be a strip of cloth unconnected to the cloth on the shoulders and chest. If it were all one piece of cloth, it would be a wimple.

There was also a version with the cloth under the chin but NOT over the head, and that was called a gorget:

As you can see, the amount of hair that needed to be covered changed across the middle ages, though in general, married women were pretty much always required to wear their hair up and neat. Loose hair was considered to indicate either a “maiden” (unmarried woman) or a “loose woman”.

Source

Daisy Ridley in Vivienne Westwood:

With John Boyega, in a  blue Agbada, a robe traditionally worn by men in West Africa, with gold detailing. A Fila, a traditional Yoruba cap, finished the look: