A cowl is a very loose neck or hood on a piece of clothing. Christian monks often wear a belted robe-like garment with a cowl.
Use the word cowl for the hood on a long, wide-sleeved garment, or to refer to the garment itself. The front of a cowl tends to be closed, rather than open like a cloak or a cape, and this was the reason cowls became the formal wear for monks during the Middle Ages — the closed cowl was warmer. Catholic and Anglican monks still wear cowls today. The Latin root of cowl is cucullus, or "hood."