What does Hebrews 7:23 mean?

In these verses, the writer of Hebrews presents several areas in which the Old Testament priesthood was flawed, or limited. The purpose of these criticisms is not to say that the Old Covenant was wrong, or bad—it was part of God's plan to bring His people to faith in Christ (Galatians 3:19—4:7). However, that system cannot be seen as the ultimate, perfect fulfillment of our salvation. Prior verses mentioned that Levitical priests received their position by ancestry, not an oath. Jesus, on the other hand, is guaranteed His role by God (Hebrews 7:21). This, in and of itself, makes His covenant better than that of the law of Moses.

Verses 23 and 24 present another way in which the Old Testament priesthood is imperfect. The law of Moses required many priests and high priests, since those men were mortal. They could not serve as priests any longer than their natural lives. Sooner or later, death would stop them from continuing in their roles, meaning those tasks would need to be passed on to someone else. Jesus, on the other hand, possesses an "indestructible" life—an eternal existence—and so He can serve as a priest forever. This is exactly what God has promised, through the priestly order of Melchizedek (Psalm 110:4).