Animals eat different type of food ranging from plants to animals.
Based on the food they consume, animals can be classified as,
  • Carnivores
  • Omnivores
  • Herbivores
Animals which are purely "meat eaters" are carnivores.  Digestion in these animals is similar to the process of digestion in human beings
Animals like lion, tiger, eagles, sharks are carnivores.
Animals which are both grass eaters as well as meat eaters are called omnivores.  Digestive system is similar to that of carnivores.
Human, bears, mouse are omnivores.
Herbivores are the animals which intake grass, roots and vegetables. Basically, these animals can be called as grass-eating animals. 
Animals like cow, goats, donkeys, deer, etc. are herbivores.
The digestion in grass eating animals is different from digestion in carnivores and human.
Digestive system in ruminants:
The below diagram shows the digestive system in herbivores. Grass eating animals have a unique digestive system when compared to other organisms. These animals have a segment called rumen, which makes the digestion in herbivores different from other animals like carnivores or omnivores..
Grass eating animals like cows chew the grass to a certain extent and it will be sent to the rumen where the grass will be digested and the digested food from rumen will again be sent back to the mouth, so that it can be chewed further. This is called rumination. Animals which have this type of digestive system are called as ruminants.
The partially chewed  food is called cud. Cows eat grass which has more cellulose. Cellulose is a hard substance to digest. Since rumen stores partially chewed food and then enable further chewing, it makes the process of digestion of cellulose easier in grass eating animals.
Rumen is a large sac like structure (muscle) present in between large intestine and small intestine.
Caecum is the portion where the digested food from the large intestine is collected and is mixed with mucus, making it easier for the absorbed contents to be mixed with mucus. It is larger in size when compared to carnivores and humans, because they consume more cellulose and water, the larger size of caecum makes the process of digestion to be easier.
Ruminant Cow: