The diaphragm contracts and this increases the volume in the lungs. If we remember gas chemistry, an increase in volume leads to a decrease in pressure, because the two are inversely proportional. Mother nature always wants pressure to be constant, so air from outside the lungs enters to equalize the external and internal pressures. During exhalation, the diaphragm expands to decrease the lung volume. This forces air out of the lungs, again to maintain an equilibrium in air pressure.