How does air flow into and out of the lungs in relation to pressure gradients?

When a person inhales, its their diaphragm pulling down and expanding their chest cavity, which causes the pressure within them to drop below ambient pressure (the pressure at their mouth) This difference is the pressure gradient, and since pressure must move from areas of high to low in an attempt to balance things out, air flows into the lungs. When exhalation begins, it is the diaphragm relaxing that causes the chest cavity to shrink, increasing the pressure to above ambient within the lungs, which forces the air out.