Because owls eat their prey whole, they require a special digestive system consisting of a two-chambered stomach: the glandular stomach and gizzard. When an owl eats its prey, the prey first passes into the glandular stomach, where acids and enzymes begin to break down its fat, muscles and internal organs.
The food then passes into the gizzard, which basically acts as a holding place for all of the materials the stomach acids can't digest, such as feathers, hair, teeth and bones. The rest of the partially digested tissues are then filtered out and continue on to the small intestine, where enzymes further break them down, with nutrients absorbed into the body. The partially digested tissues then continue on to the large intestine before eventually reaching the cloaca, where they are stored along with waste from the urinary system. The wastes are mixed with urea and eventually released from the cloaca through the owl's vent.
While this is all going on, the indigestible material remains in the gizzard, where it is slowly compressed into a pellet that is the same shape and size as the gizzard. After the gizzard compacts the pellet, the pellet then travels back to the glandular stomach where it can then be stored for up to 10 hours before the owl finally regurgitates it back up. During this time, the owl cannot eat, as the pellet blocks the entrance to the digestive system.