As far as medieval armor goes, a coif is a padded chain mail hood. A coif is usually lined with soft leather and covers the head and neck area, while leaving the face uncovered. A coif is most often combined with chain mail or heavier armor.
A more heavily armored knight will often combine a coif with a great helm for the ultimate in headgear. This also allows the knight to remove his helmet for a better view of any situation, while still maintaining some head protection.
One drawback to the coif is that is significantly muffles incoming sound. Making some communication in the heat of battle difficult.