Heart muscles get its blood supply through the coronary artery. The coronary artery is a branch of the Aorta. So the Aorta leaves the heart and branches to form the coronary artery which takes nutrients such as glucose and oxygen to the heart. The coronary artery is the red blood vessels sweeping across the surface of the heart.
If the central part (lumen) becomes blocked the heart would receive less nutrients and less oxygen. This blockage could be a partial blockage which reduces blood flow. A patient suffering from this will suffer from this is experience Angina (heart pain). A serious version of this would be where the coronary artery will completely blocked which is called Myocardial Infarction. If the coronary artery is blocked than all the heart cells supplied by the coronary artery will be deprived or oxygen and nutrients. The cells in that part will begin to die and this is what is better known as a heart attack; when severe this can lead to death. Coronary bypass is where the surgeon re-route the blockage using a extra blood vessel.