This model mimics the action of the lungs. The demonstrator’s hand performs the function of the abdominal muscles (or thoracic muscles), and the balloons, of course, are the lungs. With the diaphragm relaxed, the balloons are flaccid. When one pushes up on the diaphragm, the balloons deflate completely, and when one pulls down on the diaphragm, they inflate.
The physical principle behind this is known as Boyle's law, which states that at constant temperature, for a fixed amount of gas, pressure and volume are inversely proportional, or PV=k. In other words, if you squeeze a container of gas, lowering its volume, the pressure of the gas rises, and when you increase the volume of the container, the pressure of the gas decreases. When the diaphragm is relaxed, the pressure inside the bell jar equals the pressure outside, and the “lungs” are flaccid. When you pull down on the diaphragm, you increase the volume of the bell jar, thus lowering the pressure. Air is then forced into the “lungs” from outside, lowering the volume in the bell jar (and stretching the balloons) until the pressures inside and outside the bell jar are equal. When you push up on the diaphram, you lower the volume in the bell jar, increasing the pressure and forcing the air out of the balloons until they collapse.
Of course, in the human body, there is no air in the space between the lungs and the diaphragm, but the abdominal and thoracic muscles expand or compress the space in which the lungs sit, drawing air into the lungs or expelling it as described above.