Positive pressure ventilation and PEEP increase lung volume in 2 ways. Firstly; the positive pressure distends the alveoli, thereby increasing their volume. Secondly, the positive pressure overcomes closing pressure and recruits alveoli which would have otherwise been collapsed. These effects relevant to positive pressure in a general sense; however PEEP does most of the work. Consider that alveolar collapse is something that happens at the lowest pressure during the respiratory cycle (that would be PEEP). Also because gas exchange takes place throughout the cycle, PEEP is the pressure at which the alveoli spend more of their time, and thus the pressure which affects the diffusion surface the most.
Effect of PEEP on alveolar volume
As you increase the PEEP, alveolar volume also increases. At first this relationship is linear.
At around 10 of PEEP, the alveolus starts losing its compliance, and the relationship plateaus. Beyond 15 of PEEP, there are no further increases in alveolar diameter. Alveolar pressure continues to increase, but alveolar volume does not.
Why is this interesting? Firstly, increasing volume of the alveoli causes the overall FRC volume to increase. Secondly, an increase in alveolar diameter results in an increase of the gas exchange surface. There is more membrane to diffuse though; not only that but the capillaries running along the surface of the alveolus get stretched, allowing blood a longer time of exposure to alveolar gas. Gas exchange improves as a result. In fact, this may be the main mechanism by which PEEP improves gas exchange.
The closing volume
The FRC is the point of balance, between the urge of the lung (to collapse) and the urge of the chest wall (to spring out). At the balance of these forces, a volume of gas exists in the lungs which acts as a reservoir of oxygen.
At this volume, some of the airways are closed (some of the lung has deflated sufficiently that some of the airways close, and thus some of the alveoli are "trapped", full of air which does not communicate with the rest of the atmosphere).
Because this is the volume at which dependent small airway closure occurs, this volume is called the closing volume.
This is represented by the sad-looking collapsed alveolus in the diagram. These alveoli don't contribute to gas exchange, and they slowly empty as the gases are carried away with blood.
This situation occurs in healthy people. In disease, it is exaggerated. The sick persons lungs are even more prone to this, as the weight of the lung is increased by weight of fluid (or pus). Furthermore, the force which keeps the lungs inflated in end-expiration may be decreased or absent in a state of disease.
The elastic spring of the rib cage may be greatly diminished when the rib cage is smashed into flail segments, for instance. A pneumothorax or a pleural effusion similarly decrease the lungs ability to remain inflated, because in these conditions intrapleural pressure is no longer as negative as it needs to be. Even lying supine diminishes the normal distending pressure, because the abdominal viscera no longer pull the diaphragm down. PEEP is a force which counteracts the elastic tendency of the lungs to collapse. The airways mentioned above, which would have otherwise remained closed, are kept open. This means more alveoli are "recruited" to participate in gas exchange.
PEEP can effectively supplement the force which would have otherwise been supplied by the abdominal viscera, negative pleural pressure and chest wall recoil. Thus, PEEP can improve gas exchange by recruiting alveoli which would have otherwise remained collapsed.
How is this different to the effects of positive inspiratory pressure?
Intermittent positive inspiratory pressure can also inflate these derecruited alveoli; however this is not very nice for them. The stress of collapsing and reinflating with every breath cycle causes significant mechanical injury to the alveoli, and ultimately this ends up being counterproductive. An injured oedematous alveolus is full of fluid, and is not interested being a gas exchange surface any longer. It is now a cesspool full of airway bacteria and leukocytes, leaking inflammatory mediators into the circulation.