What is a myocardial infarction?

To answer this we can start by breaking down the phrase itself.

So, 'myo' always means muscle. 'Cardial' means of the heart. So myocardial infarction means infarction of the heart muscle.  

So what is infarction then? Infarction is a process whereby the blood flow to a tissue is so diminished that the tissue itself is damaged to the point of dying. The process of tissue death is known as necrosis.  

But why does reduced blood flow cause a tissue to die? To answer that we can look at what a tissue needs to survive - principally, it needs oxygen, the gas which we breath and all cells require to function. As oxygen is transported to tissues in the blood, reduced blood flow means that less oxygen gets to the tissue, therefore, the tissue itself dies or 'necroses'. 

So, in summary: 

Myocardial infarction is reduced blood flow to the heart muscle tissue.  This results in necrosis of the tissue due to a lack of oxygen.