The point on your face your drawing hand returns to at every full draw — usually the corner of the mouth. Without an identical anchor, every arrow lands somewhere else.
Your sight and pin are only half the aiming system — you are the other half. The anchor is your rear sight: let it drift even slightly and your whole group drifts with it, without you having touched the sight at all. That is why barebow works with three contacts instead of one: index finger in the corner of the mouth, hand against the cheekbone, string against the nose. The classic error here isn't a thinking error, it's fatigue — with too much draw weight the anchor creeps downward over a session and the group follows it. What often goes unnoticed: how much hardware helps you cross-check depends on the bow class. Compound has two mechanical checks, peep sight and kisser button; recurve keeps the kisser button — in barebow that aid is gone and the anchor is pure body work. Which is why, there, it is the first thing to go under pressure.