A bevor is a piece of plate armor designed to protect the chin and neck. When most of us think of a plate armor, we think of a helmet that completely encases the knight's head and neck, a piece called an armet. However, this fully-encasing helmet is one end point of the evolution of headgear; for many warriors, head protection was a matter of donning both a helmet and a neck/chin guard. Together, the bevor and the helmet would fully protect the head and face.
The bevor was worn with a sallet (the actual helmet), and later with a burgonet (a lighter and cheaper helmet), and would protect the chin, neck, and perhaps part of the chest. However, 'bevor' might best be translated as 'chin-guard'; the neck-guard was incorporated as a matter of convenience. The bevor was not actually connected to the helmet, although they might overlap. The bavor was in use in the 1400s and 1500s, about the same time as the armet; in England and Western Europe the sallet/bavor combination was preferred, while in Italy the armet was the headgear of choice.
Other closely related forms of armor are the gorget, which protects only the neck, the camail or aventail, which was a chain mail neck guard, and the Japanese nodowa, protecting the neck and chest. When a piece of armor covers both the neck and the chin, it may be referred to as a 'gorget and bevor', even if it consisted of one piece of plate. You may occasionally find bevor spelled 'beaver' in older documents.