We have this model of the thorax in a human body. The balloons represent the lungs. The glass jar would be where the ribs are.
Underneath there is a rubber sheet which represents the thorax.
When you pull the sheet down, you make the space bigger which lowers the pressure inside the glass jar. The air pressure outside is now bigger than the pressure inside the jar, so air forces its way in filling up the lungs. Pushing up on the diaphragm reduces the volume of the thorax, increasing the pressure. The outside air pressure hasn't changed but now finds it is at at lower pressure than the pressure in the thorax. This means that air is pushed out of the lungs.
