There's quite a bit of physics going on inside your toilet, and much of it happens within the portion of the toilet you can't see – inside the base under the tank and behind the bowl. It's mostly hollow but with a wall separating the bowl from the drain. This is what keeps a certain amount of water in the bowl between flushes. But there's more to it than that.
When you press down the handle, it lifts a lever that pulls a chain, opening the rubber flapper. Water from the tank rushes through the exposed hole and into the toilet bowl. As you see the water level rise inside the bowl, it is also rising within the base and then overflows into the drain behind it. Because no air can get past the water in the bowl, the water falling into the drain creates a siphon effect that sucks the rest of the water with it until air finally enters and breaks up the vacuum.
Meanwhile, up in the tank, fresh water is streaming in to fill it up and would overflow without some mechanism to shut off the water when it reaches a certain level. This is accomplished with something that floats – traditionally a hollow ball the size of grapefruit at the end of a rod. As the ball floats on the rising surface of the water the lever eventually shuts off the water intake valve. Your toilet may not have the big floating ball, but if you examine the mechanism you'll see that it too is based on something that floats upward and shuts off the switch.