So the bowl will flush as long as we dump enough water into it to activate the siphon. And the purpose of the tank and the flush valve is to hold and then dump about 2 gallons (7.6 L) of water very quickly into the bowl. Once the tank has emptied, the flush valve resituates itself in the bottom of the tank, covering the drain hole so the tank can be refilled. It is the job of the refill mechanism to fill the tank back up with enough water to start the whole process again.
The refill mechanism has a valve that turns the water on and off. The valve turns the water on when the filler float (or ball float) falls. The float falls when the water level in the tank drops. The filler valve (or refill valve) sends water in two directions, as shown in this figure:
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Some of the water goes down the refill tube and starts refilling the tank. The rest goes through the bowl refill tube, and down the overflow tube into the bowl. This refills the bowl slowly. As the water level in the tank rises, so does the float. Eventually the float rises far enough to turn the valve off. What would happen if the float were to become detached, or the filler valve were to jam so that it never cut off? Theoretically, the tank would overflow and flood the bathroom. But the overflow tube is there to prevent that from happening, directing the extra water into the bowl instead of onto the floor.