I guess many people get bogged down on Hebrews right about the point it gets to Melchizedek. Everything about this section - even his name - seems to say "impenetrable, time to go somewhere easier."
Here is why we should stick with it and why this man is so important to the argument. It all boils down to whether Jesus Christ can really save and declare people perfect.
Our writer's case depends on Jesus being the high priest who offered an acceptable sacrifice for sins. That exact point was under challenge. People were saying Jesus couldn't be high priest because he wasn't from the right tribe to be a priest.
Wrong tribe = not a high priest = not able to offer sacrifice = not able to present people perfect = not able to save = not God's anointed rescuer
The way to assault Christianity is always to question the identity and nature of Jesus. It all stands or falls by him. This was one of the major challenges of the day.
The writer's solution is radical. Namely that there was a priesthood prior to - and greater than - the one descended from Levi. That of Melchizedek. In other words the objection doesn't stand scrutiny. It only holds water if the aaronic priesthood was the only one, and it wasn't.
That's why we care about Melchizedek. He might be in an obscure part of the Bible but his role is critical. And just as critical is to learn from the writer to defend the major challenges of the day to the identity, nature and office of Christ. Too frequently we hear rubbish about him merely being a good teacher, or not existing, or unknowable mostly from people who don't deserve the title "academic". It is not ok for believers not to correct it whenever we hear it. To do so with gentleness for sure, but no less clearly for that.