A coif is a close-fitting cap. One style was worn by men, primarily in the Middle Ages; another style was worn by women and infants in the 16th century.
A maille coif was sometimes worn over a padded fabric coif to provide additional protection to the head and throat. This was common practice in western Europe for much of the twelfth through fourteenth centuries. Maille coifs sometimes had a "flap" of maille that could be drawn across the face and tied into place, providing additional protection.