A heart attack occurs when one of the coronary arteries becomes completely plugged. What happens is that a plaque ruptures, exposing a bare area of tissue which promotes the formation of a blood clot. The blood flow through the artery is completely stopped, so that the muscle which it supplies gets no oxygen. The pain that results from this is not only more severe than the pain of angina, but it also lasts longer, for hours rather than minutes. The amount of damage caused depends on where the blockage occurs, and whether there are other arteries supplying the affected muscle. More muscle will be damaged if the block occurs at the origin of the artery than if it's in a minor branch.
The technical name for a heart attack is myocardial infarction. Myocardium means heart muscle, and infarction means death of tissue because of a lack of blood supply. The affected muscle cells die and are eventually replaced by scar tissue. This has two effects. It weakens the heart's ability to pump, but it can also lead to an electrical instability of the heart by setting up a short circuit in the wiring. This interference with the normal, clock-like rhythm of the heart is called an arrhythmia and may take many forms. The most dangerous form, which can happen after a heart attack, is called ventricular fibrillation. Instead of proceeding through the heart muscle in an orderly fashion, the electrical impulses become chaotic, and the heart muscle quivers all over but stops pumping. This process explains why some people who have a heart attack simply drop dead, and also why emergency resuscitation can be effective, because an electrical shock administered to the chest may be able to kick the heart back into its normal rhythm.
If you're having a heart attack, it is important to get to the hospital right away. There are two reasons for this: first, the potentially lethal arrhythmias tend to occur in the first hour or two after the onset of symptoms, and second, it's possible to dissolve the clot that's blocking the artery with medications. This, however, only does any good if it's done in the first few hours, because after this, the affected muscle will already have died.