What does Hebrews 10:17 mean?

This verse comes at the end of a long discussion where the writer of Hebrews often quotes the Old Testament. The reason for these quotations is to prove that God, all along, promised to send Jesus as the ultimate fulfillment of His plan to resolve our sin. The Jewish Christians reading these words would have been especially swayed by appeals to their own Scriptures. One of the passages used was Jeremiah 31:31–34. There, God has directly said that He would form a "new covenant" with Israel, separate from the covenant given to Moses and administered by the Levitical priests (Hebrews 8:7–13). A key component of this new covenant would be its presence inside each individual person. Rather than being written on stone and dependent on repeated animal sacrifices, this new covenant would be "written" on the minds and hearts of men.

This verse quotes Jeremiah 31:34, referencing another important aspect of the new covenant. The old covenant required animal sacrifice over and over. This was not a permanent cure for sin; it was only a temporary reminder of sin and a symbol of God's ultimate plan. This new covenant, according to Jeremiah, would result in something the old covenant could not offer: actual forgiveness of sin. Jesus' single, once-for-all sacrifice for sin would actually cleanse man, from the inside, instead of merely covering his sin for a short while.