According to Boyles Law, when a gas is compressed to half its original volume the pressure exerted on the wall of the container doubles. The opposite is also true, i.e. an increase in volume results in a decrease in pressure. This law is important in understanding respiratory physiology.
During Inspiration the inspiratory muscles increase the volume of the chest with the intrapulmonary pressure falling below the atmospheric pressure. Air thus rushes in from an area of high pressure to an area of low pressure.
During Quiet Expiration, the inspiratory muscles relax and the chest wall and lung elastic tissue recoil back thus reducing the volume and increasing the pressure above that of atmospheric pressure. Air movement is thus from an area of high pressure (lungs) to an area of lower pressure (atmosphere).