What does Hebrews 8:12 mean?

This verse completes a quotation from Jeremiah 31:31–34. This is cited by the writer of Hebrews to prove that God always intended to replace the flawed "old covenant" of the Levitical priesthood with a perfect "new covenant" centered on Jesus Christ. The flaws of the old covenant were all rooted in their dependence on human beings. Part of this dependence was the need for constant sacrifice. Priests themselves were sinful (Hebrews 7:27), and died (Hebrews 7:23), and so their sacrifices could only temporarily serve to atone for sin. Jesus, on the other hand, is described as one who offers a perfect sacrifice (Hebrews 9:11–12), eternally interceding for us in heaven (Hebrews 7:24–25).

In that context, this statement about God being merciful and forgiving sins is meant to be distinguished from the work of the old covenant. Earlier statements from God, through Jeremiah, made it clear that the promised covenant was something different from what was given to Israel after leaving Egypt. God's approach to mercy and sin, here, is tied directly to this new covenant, in contrast to the old. In other words, only the new covenant can truly save us from our sins; the old covenant was never meant to.

In poetic terms, a person "forgets" or "remembers no more" when they choose to act as if something has not happened. It does not imply literal amnesia. God is not erasing our sin from His consciousness or His awareness. However, for those who accept Christ, God is able to "forget" their sins.