The function of the respiratory system is to deliver air to the lungs. Oxygen in the air diffuses out of the lungs and into the blood, while carbon dioxide diffuses in the opposite direction, out of the blood and into the lungs. External respiration is the process of gas exchange between the atmosphere and the body tissues, and includes ventilation (inhaling and exhaling air) and gas transport (the process of distributing the oxygen throughout the body and collecting CO₂ and returning it to the lungs). Internal respiration occurs inside the cell, using oxygen and glucose to generate energy (ATP), and producing waste CO₂.

The journey of the blood is also important because that’s the transport to move the gases around the body. Capillaries surrounding the alveoli pick up the oxygen, and the arteries carry oxygenated blood all around the body. The artery leads into the capillary membranes, where the blood is exposed to cells in the body that have a low concentration of oxygen and high concentration of carbon dioxide. Oxygen leaves the blood, from an area of high concentration in the blood, to an area of low concentration in the cells where it is used for internal respiration. Carbon dioxide enters the blood from an area of high concentration in the cells to an area of low concentration in the blood. The veins then return the de-oxygenated, CO₂ rich blood to the heart and then to the lungs for alveolar gas exchange.

Check out this article, which nicely summarises the transport of gases in the blood.