What does Hebrews 9:13 mean?

The running theme of the book of Hebrews is that the new covenant, in Jesus Christ, is superior to the old covenant, represented by the priests and sacrifices of the temple. Most recently, the author pointed out how components of the temple sacrifices pointed out their own limitations, and symbolized the future ministry of Jesus. A major aspect of this is the difference between the effectiveness of the sacrifices in each covenant. In the old covenant, priests offered repeated sacrifices for sins, including their own. Christ offered a single, perfect sacrifice, without Himself having any sin to be forgiven of (Hebrews 7:26–28; Hebrews 9:12).

In verses 13 and 14, the author turns his prior argument a bit upside down. Rather than arguing the faults of old covenant sacrifices, he points out that those sacrifices did have a measure of power. They could provide ritual purity to the physical flesh. If animal blood can provide that kind of benefit to a man, the power of Christ's blood would be immeasurable. As pointed out earlier, the old covenant could not resolve man's inner sin; the blood of Jesus can do just that.