The heart is a muscle, and can be strengthened like any other. This is why gradually increasing exercise is so important after heart attacks, to get the damaged muscle strengthened up again. Exercise in itself is beneficial to the heart because generally it is short-lasting, with a rest afterwards to allow the heart rate, blood pressure etc to return to normal.
However, the blood vessels are another matter - the linings are easily damaged by high blood pressure and the vessels start to fur up. This has two effects - the vessels that supply blood to the heart muscle itself (the coronary arteries) may clog up, so the heart is starved of oxygen. Secondly, the arteries carrying blood away from the heart and out to the body may also block, causing back-pressure on the heart, so every time it pumps it's having to work twice as hard. Although it can compensate to a certain extent by strengthening, it gets to the stage where it can't work any harder and starts becoming flabby and inefficient. Heart attacks are caused by a combination of clogged up arteries and a heart struggling to cope with the demand. Stressed out, in fact.