Assuming the atmospheric pressure to be constant, the relationship between intra-alveolar pressure and atmospheric pressure determines whether or not air moves into the lungs. Intrapleural pressure is the pressure within the pleural space. Due to the elastic forces of the lung (tending to contract) and the chest wall (tending to expand) under normal conditions Pip is negative. The magnitude of Pip varies with each phase of ventilation. During inspiration as the chest wall expands Pip decreases (more negative). During expiration as the chest wall recoils Pip increases (less negative). The air coming into the lung is driven by these pressure gradients.
Example with arbitrary numbers.
Inspiration: intra-alveolar pressure decreases from 0 to -1 by the action of the diaphragm and external intercostal muscles. Air will flow in until the intra-alveolar pressure returns to 0. See Boyle's law. During inspiration, intra-pleural pressure will also decrease from -4 to -6 mmHg
Expiration: Intra-alveolar pressure increases during expiration from 0 to +1. Air will flow out until the intra-alveolar pressure returns to 0. During expiration, intra-pleural pressure increases from -6 to -4.