Why does water always stay at the same level in the toilet bowl?
Because it is the same water level as the overflow height in the S or U bend of the outlet waste pipe. The extra water that is used in the flush tips over the top of the bend down the waste pipe and the remaining water that is lower stays in the bowl. The waste pipe doesn’t go straight down but goes up a little bit so that it traps water in the bowl. This water trap which provides an air lock prevents bad smells from the sewer pipe going out of the toilet and (sorry if this sounds gross) also a ready wet bowl aids faeces from sticking to the bowl. The same as the J-bend waste pipe to the kitchen sink but it is too low to fill back into the sink only a little trap in the pipe is needed.