The sacrifices of the Old Testament were for atonement of sin. Christ was the perfect sacrifice and his death was therefor the perfect atonement. Christ reconciled mankind to God.
Jesus’ sacrifice was expiation for our sins. The word expiate means to make obsolete, or to make ammends, or to remove the guilt incurred by sin.
*My little children, I am writing this to you so that you may not sin; but if any one does sin, we have an advocate with the Father, Jesus Christ the righteous; and he is the expiation for our sins, and not for ours only but also for the sins of the whole world. (1 John 2:1-2)
In this is love, not that we loved God but that he loved us and sent his Son to be the expiation for our sins. (1 John 4:10)*
Christ’s sacrifice was once, and it was for all, but we were not alive 2000 years ago in Palestine. The sacrament of reconcilliation is the way in which we are reconciled to God. The sacrament of reconcilliation is the way Christ’s atonement for our sins, his expiation for our sins, is applied to us forward in time and space.
It’s not some nebulous, spiritual, only-in-your-heart reconcillation, but like Christ’s death, the sacrament of reconcillation is something you can see, hear, feel and experience. The sacrament of reconcillation is how we know that we are reconciled to God, just like the Jews in the Old Testament knew that they were reconciled to God through animal sacrifice.
Christ took away authority from the priests, scribes and Pharisees of the Old Testament in part becasue didn’t really care about the people they were ministering to. They were in it only for the money, food, power and prestige.
Then Jesus spoke to the crowds and to his disciples, saying, “The scribes and the Pharisees have taken their seat on the chair of Moses. Therefore, do and observe all things whatsoever they tell you, but do not follow their example. For they preach but they do not practice. (Matthew 23:1-3)
Christ removed authority from the “Chair of Moses” and established the authority of the “Chair of Peter” in its stead, and to underscore the transition of power, the temple in Jerusalem which was the only place on earth where animal sacrifice was permitted by God was utterly detroyed in 70 AD. It is through the new authority of the “Chair of Peter” that we are reconciled to God.
The sacraments are how we know, beyond a shadow of a doubt.