The space under the lungs can be called as "Lung Volume" whereas force exerting by the atmosphere over an area is known as "Air Pressure"
When Contraction occurs in lungs, Volume of lung decreases, and as we know, volume is inversely proportional to Pressure, pressure inside lung increases, and expiration occurs [ Removal of gas from lungs to atmosphere ]
Now, when relaxation occurs, volume increases, pressure decreases, and inspiration occurs [ air travels from atmosphere to lungs ]
Hope this helps!
