A toilet uses a siphon to drain the water from the bowl down into the sewer system, according to HowStuffWorks. When several gallons of water are rapidly added to the toilet, it creates a pressure differential that causes the flush.
The siphon in a toilet is shaped like an upside-down U, connecting the toilet bowl to the pipes leading down to the sewer. In the toilet's resting state, most of the water does not rise from the bottom of the bowl through the siphon. However, when water is rapidly added to the toilet via either the flushing mechanism or someone pouring water into the bowl, the siphon tube fills up completely; this in turn creates a pressure differential. The pressure in the bowl at the inlet of the siphon is now higher than the tube, which causes the water to drain from the toilet through the tube. Once the water is gone, air enters the siphon to balance the pressure; this stops the drain.