The change in partial pressure from the alveoli (high concentration) to
the capillaries (low concentration) drives the oxygen into the tissue
and the carbon dioxide into the blood (high concentration) from the
tissues (low concentration), which is then returned to the lungs and
exhaled.
Once in the blood of the capillaries, the O2 binds to the
hemoglobin in red blood cells which carry it to the tissues where it
dissociates to enter the cells of the tissues.
The lungs never fully
deflate, so air that is inhaled mixes with the residual air left from
the previous respiration, resulting in a lower partial pressure of
oxygen within the alveoli.