The term 'BISHOP's Hat' is a general term used to refer to three different types of headwear worn by bishops in the Catholic Church. The first is the miter, which is a tall, pointed hat with two flat surfaces that meet at a point. The second is the MITRE, which is similar to the miter but has a rounded top and is often decorated with embroidery or jewels. The third is the BIRETTA, which is a square cap with three or four ridges on the top. All three of these hats are traditionally worn by bishops in the Catholic Church as part of their vestments.