The red blood cell has a large surface area:volume ratio and it has thin cell membranes, this allows the oxygen to diffuse quickly. The biconcave shape of the cell also increases surface area:volume ratio to maximize the amount of haemoglobin [which contains an iron ion] so it can hold to bind with more oxygen. They do not contain a nucleus, because without a nucleus, the surface area increases so there is more room to store haemoglobin to bind with oxygen. Red blood cells are also extremely small and flexible so it can fit through the capillaries/narrow blood vessels.