Answer
More than any other epistle in the New Testament, the book of Hebrews is filled with Old Testament references and imagery. It's targeting a Jewish audience, and so, grounding faith in Christ in the fulfillment of Old Testament promises is essential to the argument the author is trying to make. And so, there are a lot of references to the priesthood and the sacrificial system, even Melchizedek, because the author wants them to know that their faith is well-grounded, and not something radically new, but something radically, wonderfully old that's now fulfilled in Christ.
Answer by Dr. K. Erik Thoennes
Dr. Erik Thoennes is Professor of Biblical and Theological Studies at Talbot School of Theology