Dogster explains that dogs eat their own vomit primarily because of two reasons, the first being that their mothers fed them with regurgitated food and the second being that they smell it as food. With increased olfactory cells, dogs can smell the food particles in vomit.
Dogs Naturally Magazine explains that dogs also eat their own vomit when they have not chewed properly. The magazine notes that the canine tendency to scarf down a meal without chewing properly results in chunks of food that cannot be properly digested. When this happens, the dog's digestive system immediately rejects the food so that the dog is able to consume it again while chewing it down to a digestible texture.