Simple answer wines are living things and allowing a wine to breathe brings it to life.Wonderful things happen when a wine takes a breath. The oxygen in the air can soften tannins, aromas become more vivid, and in general a wine can seem to get better!
For reasons not known to me, each grape variety seems to have its own ideal system of oxygenation but in general younger wines benefit from decanting and the large area in contact with air softens them and makes them more drinkable quicker. If the wine is older decanting it off its sediment can work wonders and wake the wine up. It seems to help many older wines, but the process of allowing an older wine to breathe may reduce the amount of time it is at its top drinking level, so you may have to god forbid drink the bottle over a couple of hours. Like most things wine it’s a case of each bottle as it comes.