A nun's headdress is called a veil, though several items make up the headdress. The coif is the close-fitting white cap that holds the headdress in place. The wimple is the traditional white piece that covers the neck and cheeks, and the veil is the outer fabric covering.
Roman Catholic nuns vow to lead a life of poverty, chastity and obedience to God. To show modesty, consecration and membership to their order, they wear religious habits with veils as part of the ensemble; this is the origin of the idiom "take the veil," which means to become a nun. However, many modern nuns prefer a contemporary habit to the traditional one, and some choose to do away with the habit altogether while still in service.