It all hinges around two obscure obscure parts of the Old Testament, one about Abraham meeting Melchizedek. And a brief mention in the Psalms. There is more about the encounter here in Hebrews than there is in the Old Testament, which seems odd, especially as Melchizedek’s connection with the Christ is tentative at best.
The reason this was important to the original readers of Hebrews is not found in Scriptures but in the Dead Sea Scrolls. There was speculation at that time about who Melhizedek was. The importance of Melchizedek seems to be lost in antiquity.
To be brief we are back to one of the main points of Hebrews here, the Christ is better than just about anything in the Jewish religion. Here it starts with Jesus is greater than Abraham and moves on to the priesthood of Jesus is greater than the Jewish priesthood. I find it amazing that more is made here of one verse in the Psalms about the priesthood of Melchizedek than there is about the fact that the Jewish priests made sacrifices over and over again whereas Jesus sacrificed himself once, for all time and for all people.
Which means all our sins are covered. There is nothing you have done which will not be forgiven. What good news, what a wonderful God.