Here, in chapter 7, the author dives into this discussion of the priesthood of Melchizedek. The main point being made, starting here, is that Christ is the ultimate and perfect fulfillment of God's promises. So, our covenant with Him is superior in all ways to the covenant of the Levitical law. This is crucial for the letter's original audience: persecuted Jewish Christians. This idea is so important, in fact, that the author will spend a great deal of time discussing it. Of all of the explanations given in the book of Hebrews, this is the longest, running from here in chapter 7 all the way through the beginning of chapter 10 (BibleRef).