An incomplete digestive system has only one opening. The food goes in the same opening that the waste comes out. It would be as if your anus was the same opening as your mouth! Although this sounds gross, some animals make it work. Animals with this digestive system evolved early in time, and are considered pretty primitive. They don't have the fancy digestive system, or other organs that we have.
Let's look at some examples. Sea sponges may look like plants, but they are actually animals. The sea sponge filters water through its osculum, which serves as both its mouth and anus. Water goes in and special cells called choanocytes filter out food particles.
Other animals, such as the jellyfish, have a more aggressive approach. You might be aware of the dangers of stinging jellyfish from your own ocean experiences. Tentacles with stingers stun or paralyze prey, allowing the jellyfish to consume eggs, small fish, and crustaceans. The food goes into the mouth, which is also where waste exits.