By pressing the balloon, you are creating a difference in pressure between the two ends forcing the liquid to move as it is difficult to compress. When both ends are open to the air, atmospheric pressure acts equally and the liquid level will even out.
If one end of the tube is closed, atmospheric pressure changes will make the liquid move accordingly and therefore can therefore be demonstrated as a crude barometer.
Digital manometers are increasingly being used in schools and some can be connected to dataloggers to accurately measure deviations in atmospheric pressure.