Some portable toilets do indeed flush, and the ones that do are called fancy. Basic, single-occupant portables have a holding tank, as you probably have seen if you have ever used one, that eliminate flushing. The waste drops directly in. There are flushing units that have toilets that flush by using water held in a hidden reservoir inside the unit, as opposed to being hooked up to a water line like your bathroom at home. Larger portables even have sinks with water access, meaning more water reservoirs to handle the additional need.