Blood is the emphasis in this section. Old Testament Jewish worship was bloody, yet the New Testament overrules that old system of animal bloodshed by the blood of Jesus Christ for sinners. Blood still matters.
The first covenant through Moses was packed with symbolic illustrations of the Person and work of Jesus Christ. That system failed to bring sinners all the way to God, it barred us, but Christ removed the barrier.
Referencing the prophet Jeremiah, the writer points out to his Hebrew audience that their own prophet had promised a new arrangement with God, which we know is through Jesus Christ alone, a new covenant.
Our better hope is built on a better Person; our High Priest Who ministers to us not before the throne of God but on the throne of God. Jesus Christ is the reality and authority behind all of Judaism’s symbols.
Contrast between the system and priesthood of Moses, and the ministry and priesthood of Christ, are Scripturally and rationally made. Jesus brings a better hope to draw near to God by a better covenant.