What does Hebrews 7:15 mean?

Verse 13 introduced the idea that God's ideal priesthood—which He had promised in the Old Testament—was not meant to be fulfilled in the Levitical order. The author points out that the promises of the Messiah are applied to someone of the tribe of Judah (Hebrews 7:14). A change in the priestly order requires a change in the law (Hebrews 7:12), but God's promise of an eternal priesthood referred to a priestly order which came before the law of Moses (Hebrews 7:11). The conclusion of all of this, as presented here, is that God intended to bring us a high priest who would fulfill His promises—a priest like Melchizedek, not like Levi or Aaron.

The following verses will draw out the parallels between Jesus and Melchizedek. The symbolic characteristics of Melchizedek, in particular, are useful in pointing to the actual characteristics of Jesus Christ. The strongest of these, based on all of these prior arguments, is that Christ's priesthood is based on an eternal commission from God, not merely a human ancestry. Melchizedek was "priest of God Most High" (Genesis 14:18) long before the law of Moses, and God promised to establish his priesthood forever (Psalm 110:4). Christ's basis for His priesthood, as shown in the next verse, is not tied to His human heritage, but to His "indestructible" life (Hebrews 7:16).