What does Hebrews 7:12 mean?

In the Old Testament, the priesthood was established through the tribe of Levi. This came with the introduction of the law of Moses. This connection of the priesthood to a certain family line had to begin with the establishment of a new law; it could not be broken without a new law. In this chapter, the author of Hebrews seeks to prove that Melchizedek's priesthood is superior to that of Aaron, and use that comparison to show how Jesus Christ is the real, ultimate fulfillment of our salvation. As part of that argument, he has already shown that Melchizedek is a greater figure than Abraham (Hebrews 7:6–7).

This beginning and ending of a priestly line in connection to the law is crucial. Melchizedek, as later verses will point out, was not part of the tribe of Levi (Hebrews 7:6; 7:16). His was not a Levitical or Aaronic priesthood (Hebrews 7:15–16). And yet, his priesthood existed before Levi or Aaron, and his priesthood is not said to have ended. In fact, God has promised to establish someone "forever" in that very Melchizedek priesthood (Psalm 110:4). The conclusion, then, is that the Melchizedek priesthood is superior to the Levitical priesthood, and that Jesus Christ is the fulfillment of this promise.