What does Hebrews 5:6 mean?

In this passage, the writer of Hebrews explains that Jesus can serve as our High Priest because He meets all of the necessary requirements. Jesus is fully man, so He can be a priest of men (Hebrews 2:17), and He is placed in His position by God (Hebrews 5:5). In order to prove this, the writer re-uses some of the same Old Testament quotations which were cited earlier in Hebrews. This is not an accident. The writer is leading to an even greater point about who Jesus is and how the Old Testament predicted His ministry.

The quote here is from Psalm 110:4. Psalm 110 also includes the "LORD says to my Lord" verse which Jesus quoted in Matthew 22:44 and Mark 12:35–37. The entire psalm presents the King as a Priest, even though the Aaronic line was never kingly. At no point in Israel's history, prior to Christ, was the king also the high priest. And yet, other Old Testament prophets also looked forward to a time when those roles would be joined in one person (Zechariah 6:12–13). This makes Psalm 110 a prophetic vision of David, seeing the ultimate victory of a Messiah, a Priest-King, who finally defeats all of His enemies.

The writer of Hebrews is particularly interested in the figure of Melchizedek, from Genesis 14:18. Melchizedek's name means "King of Righteousness," he is described as the King of Salem, which means "peace," and is also said to be a high priest. All of this is mentioned by the writer of Hebrews to set up the point made in verses 7 through 10. This point, unfortunately, will be difficult for many of the original readers to grasp, since they are currently stuck in spiritual immaturity (Hebrews 5:11–14).