This solemn rite clearly had as its purpose to awaken feelings of repentance in the people. It was meant to bring the Israelites to the awareness of what a great evil sin is, and what punishment it would deserve.
After every sacrifice had been performed, the one who offered it was declared clean only outwardly. He could obtain inward justification only if, to his feelings of repentance, he also joined faith in the promises of God (below, Heb 11).
In that faith, if not directly and clearly, then secretly and inwardly, faith in Jesus Christ was contained.
What prophecies from the Old Testament does the Apostle cite, which foretold the abolition of the Old Testament priesthood with its inadequate sacrifices?
First, he cites the prophetic words of David the Psalmist. Through them David’s great descendant, the Messiah, as He enters the world, expresses His readiness to go and give His own body to suffering for men.
He does this after the heavenly Father is no longer pleased with Old Testament burnt offerings and sacrifices for sin (Ps 39:7-9).
Second, he repeats Jeremiah’s well-known prophecy about the coming of a new covenant. This covenant will bring with it the full remission of human sins, and therefore will abolish the whole Old Testament priestly service with its bloody sacrifices, powerless to cleanse sins (Jer 31:31-34).