What does Hebrews 7:7 mean?

Blessings are given from higher authority or power to the lower. As stated here, this is "beyond dispute," especially in the context of ancient culture. The author is making a point about how Abraham, who was blessed by Melchizedek, recognized that Melchizedek was a greater figure (Genesis 14:14–24). This is further emphasized by the fact that Abraham paid a tithe to Melchizedek (Hebrews 7:6). Since Melchizedek was a priest (Genesis 14:18), but not part of the Aaronic line, his was a different order of priesthood. This, in particular, is an important part of the symbolism of that story. The author of Hebrews will use this type of reasoning to show that Jesus Christ, not the Old Testament system of priests, is God's perfect and final plan for our salvation.

Later verses will expand this to show that Jesus' priesthood is sinless, perfect, and without end. The law of the Old Testament, on the other hand, is tied to sinful and limited people, and cannot accomplish our ultimate salvation.