What does Hebrews 10:3 mean?

For the last several chapters, the writer of Hebrews has been explaining how the new covenant is the fulfillment of God's ultimate plan for man's salvation. The old covenant was not incorrect or worthless, because it was never meant to be the final solution. Instead, each aspect of the Old Testament law was meant to foreshadow some aspect of Christ's ministry. Even the sacrifices, themselves, were intended to prove that animal blood, offered by sinful priests, could never truly cleanse mankind from their sins (Hebrews 9:8–10).

Here, the writer gives a more direct explanation for what these animal sacrifices actually did. The fact that the priests offered them over and over proved that sin had not been truly dealt with. It had been "covered," but not "cleansed." In the prior verse, the writer made the point that if an animal sacrifice could truly pay for sin, there would have been no reason to keep offering that sacrifice!

This leads into an idea explained over the next few verses, and supported by more quotations from the Old Testament. The sacrifice of Jesus Christ was a single, once-for-all-time event. This was able to accomplish what animal blood could not: actual forgiveness of sins, and a change in the inner nature of man.