Coifs were fairly simple head coverings, made in 1 - 3 pieces. Both men and women wore them. They were worn at night to keep the head warm, in the day to protect the head from the sun, or under knights' helmets to soak up sweat. It was worn before the 1500's, except for the 3-piece, which was more popular during the 1500s. It was tied by ties attached to the front corners.

The term "coif" is also sometimes used for a knight's chain mail hood.

For further information:

How to Make a Coif