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In the alveoli, oxygen from the air is absorbed into the blood. Carbon dioxide, a waste product of metabolism, travels from the blood to the alveoli, where it can be exhaled. Between the alveoli is a thin layer of cells called the interstitium, which contains blood vessels and cells that help support the alveoli.
The alveoli are surrounded by capillaries, and since each of these are a single-cell layer thick (increadibly thin!), the oxygen and carbon dioxide can pass from the alveolus to the blood (and CO2 comes out the other way).