Reconciliation; restoration of friendly relations; agreement; concord., Satisfaction or reparation made by giving an equivalent for an injury, or by doing of suffering that which will be received in satisfaction for an offense or injury; expiation; amends; -- with for. Specifically, in theology: The expiation of sin made by the obedience, personal suffering, and death of Christ.

The ancient Mosaic law required the blood sacrifice of animals for the expiation and atonement for sin.

www.dictionary.com/ says "the means by which atonement or reparation is made."

I think you mean atonement and it means an amends or reparation made for an injury or wrong; expiation.

The root word of expiation is "expiate," which means to make amends or atone for wrongdoing. It is derived from the Latin word "expiare," meaning to make satisfaction or to cleanse from guilt.