What does Psalm 103:12 mean?

In love and mercy, the Lord has removed His people's sins from them. He doesn't simply move our sins onto our doorstep or a mile away; God moves them as far from us as the east is from the west.

This is an especially profound analogy. North meets south at the South Pole, and south meets north at the North Pole. East and west never meet—there is neither an east pole nor a west pole. A person who follows a straight path north will eventually begin moving south. But no matter how far one travels east, they will always be moving east. North and south are definable points, but east and west are indefinitely far from each other. To say that God separates our sins "as far as the east is from the west" speaks of the absolute, irrevocable measure by which God forgives us.

On Israel's annual Day of Atonement the high priest killed a bull as a sin offering for himself and his household. He also sacrificed a goat for the people of Israel. A second goat became the scapegoat. The high priest laid his hands on this animals' head and confessed all Israel's iniquities, transgressions, and sins. Then he sent the scapegoat into the wilderness, where it symbolically carried the nation's sins over the horizon, never to return. Thus, the people's sins were removed far from them (Leviticus 16).

If we were to search for the sins the Lord has removed from us, we would never find them, because Jesus, the Lamb of God, has taken them far away (John 1:29) from those who come to Him in faith (John 3:16–18). When we turn away from that gift, we resign ourselves to bear punishment for sins ourselves (Acts 4:12; John 14:6).