When you flush the toilet on a cruise ship or use the sinks, showers etc the water goes into a sewage tank underneath the rooms in the ship.
The cruise ships sewage tanks are in the bowels of the cruise ship and they have ways of treating the sewage before it's released.
The cruise ship can release the sewage though untreated if they are 12 miles away from land so they can dump the untreated sewage into the ocean as they are traveling down the ocean.
That seems gross but it's not really a bad thing as the sewage will be naturally treated in the ocean just like when sewage is on the ground the earth naturally treats the urine and poop.
So cruise ships do dump human waste into the ocean as well as foods scraps and sometimes other trash.