What does Hebrews 9:21 mean?

This verse refers to a time in the Old Testament when Moses first introduced God's commands to the people of Israel. This is found in Exodus 24:6–8, as well as portions of chapter 29. Even from the very beginning, blood was necessary to "inaugurate" a covenant. This is mentioned for two purposes. First, this idea leads into the summary given in verse 22, that bloodshed is absolutely required for forgiveness of sins (Leviticus 17:11). Second, the blood shed by Jesus Christ accomplishes what the blood of animals never could.

Previously, the writer of Hebrews had mentioned that the animal sacrifices used in the old covenant were imperfect. They could temporarily cover the sins of the people. But those sacrifices could not change a person's nature, or completely remove the penalty of their sin. Christ's sacrifice, on the other hand, was a once-for-all shedding of blood, which can perfectly and permanently save mankind. This new covenant is exactly what God had intended all along, and had promised in His own Word. The old covenant was intended to symbolize this ultimate plan.