The alveolar epithelium is very thin, just one cell layer thick. This means the diffustion distance is small, therefore diffusion of gases occurs rapidly.
Remember that diffusion is the net movement of particules from an area of high concentration to one where its concentration is lower.
Diffusion will be faster if there is a greater difference in concentration between the two areas. This is known as the concentration gradient. A steep concentration gradient will increase diffusion rate.
Each alveolus is highly vasculated (many capillaries surround the alveolus). This mantains a steep concentration gradient. Once blood adjacent to the alveolus has been oxygenated, it is rapidly removed by action of the heart, and replaced with deoxygenated blood.
Similarly, the lungs maintain oxygen rich air in the alveoli through the process of ventilation.