What does Hebrews 8:10 mean?

This verse continues a quotation from Jeremiah 31:31–34. The writer of Hebrews is pointing out that God Himself promised to give the people a "new covenant." Logically, then, this means that the old covenant is inferior to whatever God has planned for the future. If it was not, why would He change it? This is part of the argument that God's intent was always for salvation to come through Jesus Christ, not through the Old Testament Law. Prior verses proved that this promised covenant was new, not merely a re-use of the old, and that the primary weakness of the old covenant was its reliance on human efforts.

In this verse, Jeremiah describes a new covenant between God and man which perfectly describes the ministry of Jesus Christ. In particular, this verse points out the difference between a covenant based on external, legalistic rules and one based on internal, personal experience with God. This drive for obedience, from the inside out, is the work of the Holy Spirit in those who are saved (2 Corinthians 3:1–3). Jeremiah was not the only prophet to make such a claim; the idea is also seen in places such as Ezekiel 36:26–27.