This isn't the easiest letter to read. Why? It centers around the significance and detailed work of Levitical priests. One of the points of this letter is to help the Hebrew people see that Jesus is a superior high priest compared to the Levites. Because of the reverence and devotion given to the Levitical high priest, this author is arguing that now it can be given to Jesus.
In the Scriptures for this week, the author is using the high priest Melchizedek (read about him in Genesis 14 - neat story) to bolster his argument. Basically, if the OT shows that there already exists a superior high priest in Melchizedek over the Levites, then it is possible for God to send a new high priest superior to Melchizedek. It's a sly argument.
It's important to note that the Hebrew community to which this letter is being written is very devoted to their God. They likely follow the Torah devoutly. But they are struggling with what to do with Jesus. How does he fit into God's current (at that time) revelation? The author does a masterful job of tying OT elements together, especially the poem from Jeremiah 31 - about the new covenant, Jesus is the new high priest for the new covenant God plans to establish.
The more you understand the Book of Leviticus, the more you'll appreciate the argument being made in this book. It just takes time, and the deeper you dig, the more treasures you discover.
Jesus came to save the world, but he started with the Hebrews. He came as a Hebrew to the Hebrews. The first converts were Hebrews. When Paul (a fiercly devout and brilliant Hebrew) went to the far reaches of the Roman Empire with the Gospel, most of his converts were Hebrews, along with another special group of people (which is where we fit in): God-fearers.
There were many, many Gentile men and women around the Empire that had abandoned their local or national religions in despair, and had sought to know the God of the Heberw people. Because they were Gentiles, they could not become Hebrews - this limited their involvement in the Temple rituals and other religious practices. But there was a special place for Gentiles who wanted to worship the Heberew God. So in synagogues (teaching facilities for Hebrews established in every city) where Paul would teach about the Hebrew Rabbi Jesus, many, many, many God-fearers believed and were saved. If you've read through Acts, you'll see that after awhile, more God-fearers were believing in Jesus then Hebrews.
One implication of this history lesson (and brief overview of the Letter to the Hebrews): understanding the original covenant that God cut with Abraham, Isaac, Jacob and David is vital to your vibrant understanding of the new covenant that God cuts with us through Jesus. The less you understand about the OT, the less you understand about the Gospels and the NT.
Can you still be saved with a minimal understanding of the OT and NT: sure, it happens all the time. But who wants to go through life with minimal understanding of what we consider the source of life and our greatest delight?
God says in the Psalms: delight in me and I will give you the desires of your heart. Jesus says in the Gospels: obey my commands (to love one another) and I will make your joy complete.
I'm in; how about you?