Chew the greenery is a phrase used to describe the behavior of animals such as cows, sheep, and goats, who eat grass and other plants. Grazing is the act of an animal feeding on grass or other vegetation in a field or pasture, while CUD is the food that is regurgitated and chewed again by a ruminant animal. Therefore, chew the greenery is a phrase that describes the process of grazing and CUD-chewing that these animals do in order to digest their food.