The aorta carries oxygen-rich blood away from the heart to the rest of the body. A section of the aorta curves right back towards the heart, and splits into the left and right coronary arteries, which are vessels that carry the oxygen-rich blood to the heart muscle itself. The left coronary artery is called the left main coronary, which then branches into the left anterior descending coronary artery and the left circumflex coronary artery. All of these eventually branch down into capillaries, which the blood flows through to feed the heart muscle. The de-oxygenated blood within the heart muscle then begins its return trip through the cardiac veins, which lead to the right ventricle of the heart, which collects all the de-oxygenated blood from the body.
The blood that does not circulate to support the heart itself is either pumped through the pulmonary circulatory system or the systemic circulatory system. The systemic consists of the inferior and superior vena cava, which transports de-oxygenated blood from the body to the heart. The pulmonary system consists of the pulmonary veins and arteries, which transports the oxygen-rich blood from the lungs to the heart, and oxygen poor blood from the heart to the lungs. See graphics at the links:
For more information on the different parts of the artery, including helpful diagrams, see the link below.