Readers of Leviticus will know that animal sacrifices make “atonement” for Israel’s sins. It is common for English readers to understand the goal of atonement by parsing the word’s superficial parts: “at-one-ment.” That is, the blood of the animal through sacrifice puts God and humanity “at one” in their relationship. However, this is not what the underlying Hebrew means. Instead, of indicating a repaired rift in divine-human relationality, the original "atonement" language of Leviticus refers to the purging of sin through blood.
In biblical thought, “sin” (חטא; hatta) or “iniquity” (עון; avon) is a physical substance that clings to sinners and saddles them with a death-dealing weight. Sin is a sticky, polluting stain that can adhere to human beings, the altar, the temple, and even the land itself. This is why “atonement” must be made for the altar (e.g., Exodus 29:36-37) and the land must be atoned for after a murder (see Numbers 35:33). If left unchecked, the plaque of sin can become so voluminous that it can build up on the temple and push God out of the holy abode. As the Lord says to Ezekiel, “Son of man, do you see what [my people] are doing, the great abominations that the house of Israel are committing here, to drive me far from my sanctuary?” (Ezek 8:6). When God has to leave the temple due to incoming sin (see Ezek 11:22-23), this divine absence leaves the temple open to attack, which is why the Babylonians were able to sack Jerusalem and destroy Solomon’s temple in 586 BCE.
The Hebrew word translated “atone” is כפר (kipper), which means to “purge” or “expunge.” The act of atonement is not synonymous with “restoring relationship”—though proper divine-human relationship is a corollary of atonement. Instead, to atone is to purge the people and land of its polluting sin and get rid of the burden that weighs on the world. Leviticus says that on the Day of Atonement “purgation (יכפר; yekhaper) shall be [done] for you to cleanse you, and you shall be clean before the Lord from all your sins (חטאתיכם; hattotekhem)” (Lev 16:30). Once sin is purged, God forgives sinners based on that atonement. When Matthew says that Jesus will “save his people from their sins” (1:21), the Gospel means that the Messiah will “pour out” his own “blood” (26:28) to eliminate the burden of iniquity.