Angina: officially Angina Pectoris, from latin and greek meaning 'squeezing of the chest'. Chest pain characteristic of ischemia (lack of blood and oxygen) to the heart muscle. Frequently described as a tightness in the mid chest with radiation to the arm or neck. The actual symptoms can vary widely, and in fact many people (especially diabetics) can have 'silent' angina and have ischemia or even a heart attack and just feel 'bad', with no specific chest discomfort. Angina is most often caused by a narrowing in one or more of the coronary arteries. These vessels supply the blood to the heart muscle itself. Prolonged lack of blood and oxygen to an area of heart muscle leads to the death of muscle cells (think permanent irreversible damage) = Heart Attack.
Angina itself is not a heart attack. The pain is usually relatively short in duration and with cessation of the inciting activity will subside and adequate perfusion to the involved heart muscle cells return. Stable angina is characterized by a repeatable set of symptoms, typically chest discomfort that occurs with physical exertion and will be relievable with rest. It may progress to occurring with less activity and in severe cases may even occur at rest or wake one from sleep. Symptoms that are progressive are then referred to as "Unstable" angina. Rest and especially nocturnal angina are most concerning since they frequently are characteristic of severe coronary artery disease.
The important 'take away' is that any chest pain should not be ignored. In the case of a heart attack "time is muscle' and the sooner attention is sought and perfusion restored to the heart muscle in jeopardy (via drugs or mechanical treatments) the less permanent damage occurs.