What does Hebrews 8:8 mean?

This begins a quotation from another Old Testament prophet, found in Jeremiah 31:31–34. This is used to support the writer's claim that God promised a "better" covenant than the Old Testament system of priests and sacrifices. Earlier in this letter, the writer of Hebrews offered passages such as Genesis 14 and Psalm 110 to show this promise. Here, he introduces yet another place in Jewish Scripture where God explicitly says He will one day replace the Levitical priesthood with something superior.

The language used by Jeremiah is very clear: this is a "new covenant," something meant to replace the "old covenant." Further, Jeremiah's statement is forward-looking. This is a promise God made which was meant to be fulfilled at some later date. Jeremiah was not looking into the past, at some decree God had made long ago. This was, at the time, a new statement from God. The reference to the people of Israel, as well as the house of Judah, emphasizes that this is part of God's plan for His chosen people, one which would be extended to the rest of the world through Jesus Christ (Romans 3:20; 5:12).