The boom tends to lift while sailing, especially when the main sheet is eased to fall off the wind. As the boom rises, the top of the sail will twist and spill wind. A boom vang connects the middle of the boom to the base of the mast and keeps the boom from rising. It can be a block and tackle or a solid piece of gear. To the extent that the main sheet controls side to side motion of the boom, the vang controls up and down motion.
As you ease the main sheet, a properly trimmed vang will take over the task of maintaining leech tension and will keep the sail from getting too loose. It will also keep the boom from bouncing in waves and make the sail trim more stable and consistent.
When beating close hauled, the sheet holds the boom down and the vang can be loose or lightly tensioned. Harden it up when falling off to a reach, to counteract twist, and keep it quite firm while running. Do not over tighten the vang, especially in high winds. Too much vang tension will flatten the sail, stress the rigging and make the boat harder to steer.