Christ is our Mediator through His blood; by it our conscience, is freed from sin in the sight of God. Martin Luther writes in this excerpt to help us understand:
But when Christ appeared as a high priest of the good things that have come, then through the greater and more perfect tent (not made with hands, that is, not of this creation) he entered once for all into the holy places, not by means of the blood of goats and calves but by means of his own blood, thus securing an eternal redemption. For if the blood of goats and bulls, and the sprinkling of defiled persons with the ashes of a heifer, sanctify for the purification of the flesh, how much more will the blood of Christ, who through the eternal Spirit offered himself without blemish to God, purify our conscience from dead works to serve the living God. Therefore he is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance, since a death has occurred that redeems them from the transgressions committed under the first covenant. (Hebrews 9:11-15 ESV)
According to Leviticus 16, the high priest must once a year enter into the holy place with the blood of rams and other offerings, and with these make formal reconciliation for the people. This ceremony typified that Christ, the true Priest, should once die for us, to obtain for us the true atonement. But the former sacrifice, having to be repeated every year, was but a temporary and imperfect atonement; it did not eternally suffice, as does the atonement of Christ. For though we fall and sin repeatedly, we have confidence that the blood of Christ does not fall, or sin; it remains steadfast before God, and the expiation is perpetual and eternal. Under its sway grace is perpetually renewed, without work or merit on our part, provided we do not stand aloof in unbelief.
Christ, in God’s sight, purifies the conscience of dead works; that is, of sins meriting death, and of works performed in sin and therefore dead. Christ purifies from these, that we may serve the living God by living works. (“Christ Our Great High Priest”)