At home, you press the handle and water gurgles into the bowl. Most residential toilets flush by gravity. The storage tank sits above the bowl so that the natural, downward pressure of the water makes it flow into the bowl after you press the handle. In most public restrooms, on the other hand, there's no storage tank. That means that water flows into the bowl not by gravity, but under pressure from the water pipe.
Pipes deliver water to homes and businesses at a higher pressure than the air outside.
When you flush a public toilet, the water bursts forth at a high velocity because of the difference in pressure between the pipe and the bowl. In the bowl, the pressure is much lower than it was in the pipe, causing the water to rush in forcefully. Even though a pressurized flush may look like a river of churning whitewater, it doesn't require any more water than a gravity flush. That's because it's the pressure of the water, not the volume, that increases the water's velocity. And if that's not enough of the physics of flushing for you, here's more.