I've always found Hebrews very difficult to undertstand. My problem has been that I've read it like a theological essay.
I realized this week that this letter is simply a sermon (13:22). It's very pastoral and basically has one objective: to encourage the readers to persevere in the faith. Let me offer a few helps as you read it.
The writer is writing to Jews ready to give up their faith for Old Covenant religion. He appeals to his readers in a variety of ways. First, he tries to demonstrate the exaltation or worth of Christ (Ch. 1-3, 4b, 5, 7). He then tries to incite them with the promises offered by God through Jesus (Ch. 4, 8, 12b). In addition, he repeatedly makes clear the dangers of falling away from the faith. Like a good pastor, he warns them of this (such as in Ch 6, 10). Also, he helps them to see how others have succeeded in faith in the past (Heb. 11). Not only that, but we should consider Jesus' perseverence amid much suffering (Ch. 12:1-3) . The writer finally explains the meaning of their trials, for we can usually endure hardship if we see the purpose (Ch. 12). Lastly, the writer of Hebrews offers some practical ways they can live holy lives (Ch. 13). It is noteworthy as well to see that the closing prayer of benediction well summarizes these points (13:20-21).