What does Hebrews 9:12 mean?

Earlier, the writer of Hebrews compared the continual sacrifice of the temple priests with the offering a true, heavenly high priest would offer (Hebrews 7:22–28). In doing so, two separate Greek words were used. The term referring to the priests implied a present, ongoing action. The term referring to Jesus used a completed, once-for-all action. Here, that same idea is once again attached to Jesus' sacrifice. The phrases used in this verse echo the same points made earlier in Hebrews about Jesus.

The earthly high priests of the old covenant offered sacrifices on a yearly basis (Hebrews 9:7), taken from mere animals, in a temporary sacrifice, including atonement for their own sins (Hebrews 7:27), which only served to assuage external factors, and could not change the hearts of men (Hebrews 9:9–10).

The heavenly high priest of the new covenant—Jesus Christ—offered a single sacrifice, once and for all, taken from His own perfect and sinless life (Hebrews 4:15), completely saving mankind from their sins (Hebrews 7:25), changing them from the inside out (Hebrews 8:10).

Another point being made here is that animal blood can never fully atone for human sin—only the blood of a man can do that, and this is exactly what Jesus provides.

The next verses will emphasize and expand on the difference between the sacrificial blood of animals and that of Jesus. Prior emphasis was on the limitation of those animal sacrifices; as this passage continues, the emphasis will be on how Christ's blood possesses far greater power than that of any animal.