A flexible, conical, brimless, head-dress, enveloping the entire head except the face, and worn either as a separate garment or as part of a cloak.
Under the Roman Empire it was separate but both styles were used during the Middle Ages.
It was the customary head-dress of monks and mendicant friars, and constituted part of the religious habit.
The hood of the 13th and 14th centuries, called liripippium, usually formed a long peak, extending down the back, and frequently served as a neck-cloth.
It has been retained by the old Orders ever since the adoption of hats by both clerics and laymen.
New Catholic Dictionary