What does Acts 2:34 mean?

Peter is continuing his argument that David's prophecies give key identifying characteristics of the Jewish Messiah. First, Peter used Psalm 16:8–11 to show that someone David called his Lord would die and be raised again by God (Acts 2:25–28). Peter explains that this can't be David because after David died he was buried, and everyone knows where his grave is (Acts 2:29). No, the "Holy One" is Jesus, and the 120 Galileans standing before the crowd are witnesses to Jesus' resurrection (Acts 2:32).

Now, Peter goes to a passage that he'd heard Jesus use to show the Messiah, or Christ, is greater than David. It was custom at that time for Jews to refer to the Messiah as the "Son of David." God promised David that he would have an heir that would rule on David's throne forever (2 Samuel 7:16). This heir will free Israel from oppression and rule in peace (Isaiah 9:1–7). It's true that as David's descendant, the Messiah would be his biological "son"—many times removed. And Jesus is descended from David through both adoption by Joseph (Matthew 1:6–16) and by birth through Mary (Luke 3:23–32). But the scribes use the term "Son of David" to mean David's heir is somehow subordinate to David.

Jesus has already used Psalm 110:1, quoted in Acts 2:34-35 to show this is not the case (Mark 12:35–37). As Jesus explained, "David himself calls him Lord. So how is he his son?" (Mark 12:37). The first "Lord" is God the Father, the second "Lord" is the Messiah, the heir of David. David is submitting to his own heir.

The second line further shows David is not speaking of himself. Not only did David not rise from the dead, he certainly didn't ascend to heaven and take the seat at God's right hand. The seat to the right hand of a ruler is reserved for that ruler's most trusted advisor. The right hand represents authority and strength. David had no delusions that he belongs at the right hand of God, but, while on trial in front of the Sanhedrin, Jesus claimed He does (Luke 22:69).