The circulatory system describes the system of arteries, veins, and capillaries that allows blood to reach every part of the body. The proof of this system was discovered by William Harvey in the 17th century, and is widely credited with being one of the discoveries that set off the scientific revolution in Europe.
Starting in the heart, blood is pumped into the aorta, where smaller arteries branch off to reach the head, arms, legs, and torso. The arteries become narrower until they are one blood cell wide - the capillaries. It is at this level that they exchange oxygen for carbon dioxide. The capillaries then merge into veins, which eventually become larger and larger until they reach the heart again. This cycle takes about one minute in the average adult human.
Once blood from veins is returned to the heart, it's pumped into capillaries in the lungs through the pulmonary artery to reoxygenate it, and is returned to the heart through the pulmonary vein. The cycle then starts again.
Blood in arteries is moved by the pressure of the beating heart. Blood in veins is moved by the contraction of muscles surrounding the veins. The existence of one-way valves in the veins forces the blood to flow towards the heart. The breakdown of such valves leads to varicose veins.