The coronary artery is the artery that carries blood to the heart. Specifically, the coronary arteries branch off from the base of the aorta and supply oxygenated blood to the heart muscle (myocardium) itself. Without this blood supply, the cardiac muscle cells would not receive the oxygen and nutrients they need to function, which is why blockage of the coronary arteries leads to a heart attack (myocardial infarction).
The pulmonary artery carries deoxygenated blood from the right ventricle of the heart to the lungs for gas exchange. The renal artery carries blood from the aorta to the kidneys. The aorta is the largest artery in the body and carries oxygenated blood away from the left ventricle to the rest of the body.
A common source of confusion is thinking that "carries blood to the heart" means veins (since veins generally return blood to the heart). However, the coronary arteries specifically deliver arterial blood to nourish the heart tissue itself.