At rest, the heart uses almost all of the oxygen delivered to it via it's own vessels, the coronary arteries. When the heart is subjected to an increased workload, these vessels dilate in response. If a vessel is occluded with plaque or a clot, it will be unable to supply the blood and oxygen needed, and pain and tissue damage can result.
The key determinants of myocardial (heart muscle) oxygen demand are myocardial contractility, heart rate, and very importantly- myocardial wall tension.
Nitroglycerin is, at typical doses, a VENOUS dilator. By decreasing venous return to the heart (preload) nitroglycerin decreases the filling pressure of the heart, decreasing myocardial wall tension, force of contraction, and by extension, myocardial workload and oxygen demand of the stressed tissue. Nitroglycerin only minor effect on arteries or arterioles at usual doses, although a high dose drip (greater than 40mcg/min) can have artery dilating effects. So, nitro does not dilate atherosclerotic arteries to allow blood to flow around any clots or occlusions in the arterial system of the heart. When nitroglycerin has been injected directly into a blocked coronary artery, it has not relieved pain! In other words, nitroglycerin eases coronary chest pain by reducing the heart's oxygen needs, NOT by providing more oxygen supply. Although blood pressure can drop with nitroglycerin, it can be minimized with the patient lying down.
There are drugs that selectively dilate arterioles, (reducing afterload) like hydralazine and minoxidil, which are very powerful at reducing blood pressure. These drugs are NOT used in acute anginal pain, because, as blood pressure drops with them, there is reflex tachycardia and increased myocardial contractility, greatly increasing the workload and oxygen demand of the heart. Although the drop in blood pressure with nitroglycerin can also cause tachycardia, it is generally milder, and often eliminated with a beta blocker medication to prevent it.