Actually, its a myth that owls can rotate their heads 360 degrees. In reality, they can only rotate their heads by up to 270 degrees.
Unlike human beings and almost all other animals, owls have fixed eye sockets and hence are unable to move their eyes to follow movement or use peripheral vision. They are forced to move their heads for such purposes. Owls are adapted to these limitations and have anatomical differences to support this wide movement of the head. Unlike human beings, who have two pivot sockets to connect to the head, owls have only one such socket. In addition, owls have multiple vertebrates and backup arteries. Their blood vessels also grow larger as they branch, which ensures blood supply even with such extended head movements.