Looks like a coif, which could be tied under the chin and was often worn as a type of hat. Came into existence circa 1000 AD/CE and used by men & women, with men stopping usage circa 1400 AD/CE. For men, there were some other versions made to be worn either as a part of armour (chain mail coif), or a liner to be worn under armour (a leather/quilted cloth coif worn under a helmet).