A myocardial infarction
(or what is commonly referred to as a "heart attack") means that some portion of the heart muscles has died due to inadequate blood flow. This may be a very small area or a very big one, but there is no way to cure a myocardial infarction. You are correct - once heart muscle dies, it is dead and does not regenerate. Instead, it becomes scar tissue.
Right now, there is a lot of research looking at delivering stem cells to the infarcted area (the scar) in order to promote the growth of new muscle, but the results have not been terribly exciting so far.
Even though we can't cure a myocardial infarction/heart attack (yet), though, we can TREAT it in order to reduce the risk of another heart attack and to get the patient back to as normal a life as possible. Hope that is helpful!