Hebrews 9:21-22
And in the same way he sprinkled with the blood both the tent and all the vessels used in worship. Indeed, under the law almost everything is purified with blood, and without the shedding of blood there is no forgiveness of sins.

After Moses received the law (including the ten commandments) from God, the people of Israel agreed to obey all that the Lord had commanded. In Exodus 25:3-8, the covenant is confirmed by offering sacrifices of oxen, and then placing the blood on the altar and the people. As he did this, Moses said "Behold the blood of the covenant that the Lord has made with you in accordance with all these words."

Many centuries later, as Jesus ate with his disciples in the upper room, this took place: Now as they were eating, Jesus took bread, and after blessing it broke it and gave it to the disciples, and said, "Take, eat; this is my body." And he took a cup, and when he had given thanks he gave it to them saying, "Drink of it, all of you, for this is my blood of the covenant, which is poured out for many for the forgiveness of sins." [Matthew 26:26-28]

Did you notice the common phrase? The "blood of the covenant" is present in both the old and new covenants, for as the writer of Hebrews has reminded us today, "without the shedding of blood there is no forgiveness of sins."

Our forgiveness is only possible because our sin has been punished. The proper punishment for sin is death [Romans 6:20-23], but as Isaiah 53 details for us, God's chosen one (the Messiah) died that death on our behalf. He bore the wounds that rightfully should have been ours. He suffered and died, and the punishment that brings us peace was upon him.

It is the blood of Jesus that makes forgiveness possible, as it has appeased God's righteous wrath against our sin. The sacrifices in the old covenant were done in anticipation of the Messiah, just as the Lord's Supper is taken in remembrance of Him.