Arteries and veins are responsible for transporting blood from the heart to the capillaries and from the capillaries back to the heart.
Capillaries are the site of exchange of nutrients where arterial blood (oxygenated and nutrient rich) is transformed into venous blood (deficient in oxygen and nutrients and rich in carbon dioxide and waste products).
Exchange of respiratory gases and nutrients between capillaries and tissue cells takes place by simple diffusion, a process which is only efficient over short distances (<5µm). In order to ensure that blood is transported to within a diffusible distance of all cells we need a highly complex network of blood vessels.