29 Men and brethren, let me freely speak unto you of the patriarch David, that he is both dead and buried, and his sepulcher is with us unto this day.
30 Therefore being a prophet, and knowing that God had sworn with an oath to him, that of the fruit of his loins, according to the flesh, he would raise up Christ to sit on his throne;
31 He seeing this before spake of the resurrection of Christ, that His soul was not left in hell, neither His flesh did see corruption.
32 This Jesus hath God raised up, whereof we all are witnesses.
33 Therefore being by the right hand of God exalted, and having received of the Father the promise of the Holy Spirit, He hath shed forth this, which ye now see and hear.
34 For David is not ascended into the heavens: but he saith himself, The Lord said unto My Lord, Sit thou on My right hand,
35 Until I make Thy foes Thy footstool.
36 Therefore let all the house of Israel know assuredly, that God hath made that same Jesus, whom ye have crucified, both Lord and Christ.
Peter is explaining that David could not have been writing about himself in Psalm 16. David was long dead and still in his grave. David was referring to his descendant, Jesus Christ, who did fulfill the prophecy, as they had all witnessed. David had not ascended into heaven as he wrote, and Peter quotes in Psalm 110:1 (also quoted in 1 Corinthians 15:25 and Hebrew 1:13 and 10:13).
As a servant, Christ had won victory on the first plane; He had not originated evil. As man He had won victory on the second plane; He had overcome evil in its assaults from without. He now said: I am going into death, but death cannot hold Me. Death is the wage of sin. Death is that which has resulted from the fact of rebellion against God. I am going into it, but it cannot hold Me: Thou wilt not leave My soul in Hades, Neither wilt Thou give Thy Holy One to see corruption. — Morgan, pg. 76.
None of the rabbis ever thought of applying the psalm to the promised Messiah. There is, however, an old tradition, which no doubt was known and believed in that day, which applied the psalm literally to David. This application was as follows; “Those words, ‘my flesh shall rest in hope,’ teach us that neither worm nor insect had any power over David.” Peter shows that such a traditional belief that the words referred to David himself were incorrect. They could not mean King David. — Gaebelein, pg. 58.
brethren, let me speak freely (v.29) — Peter’s bold message was given with gentleness. freely = with boldness of speech
patriarch (v.29) — father or chief of a race. David is the ancestor of the royal line of the Jews.
David is dead and buried (v.29), so Psalm 16 couldn’t apply to him when it speaks of Hades.
sepulcher (v.29) — David’s sepulcher — Nehemiah 3:16
God swore with an oath (v.30) — Psalm 132:11
seeing this before (v.31) — looking into the future
The resurrection of Christ (v.31) — Peter’s argument was clear, consecutive and forcible. It ran as follows.
The words of Psalm 16 about the resurrection refer definitely to someone.
They cannot denote David, for he died and saw corruption.
But, as all Jews acknowledged, the Messiah was promised as prince of the house of David.
The Psalm, therefore, refers to the Messiah.
Jesus of Nazareth was raised from the dead, and so He is the expected Messiah. — Walker, pg. 50.