The process by which gasses pass between capillaries and body cells (such as those for tissues and organs) is called gas diffusion. Capillaries are a part of the circulatory system whereby blood is pumped from the lungs through the heart and then throughout the body's system of blood vessels to deliver nutrients and remove waste from the body's cells. The blood leaves the heart through the aorta which eventually branches out and narrows down to various tiny capillaries (which are the smallest of blood vessels) which then connect with veins that carry the used bloodstream back to the heart and lungs.
In terms of gasses, the circulatory system is responsible for transporting oxygen from the lungs to all of the cells in the body. It also picks up carbon dioxide as a waste product from the cells and transports it back to the lungs for expulsion from the body via exhaling. These gasses pass in and out of the bloodstream via diffusion along a concentration gradient. The gasses diffuses from the oxygen rich capillaries to the oxygen poor body cells. Likewise, the carbon dioxide diffuses from the cells to the blood in the capillaries. The diffusion occurs from areas of high concentration to low concentration. This diffusion is possible because the endothelium lining of the capillaries is extremely thin, sometimes only one cell thick. This allows the gas molecules to pass through the capillary lining with relative ease.