What does Acts 2:31 mean?
Peter is using David's prophecy of Psalm 16:8–11 to explain that Jesus of Nazareth is David's heir who will sit on his throne for eternity. Near the end of a psalm wherein David speaks for himself, there is one verse where he speaks for his Lord (Psalm 16:10). This verse can't apply to David; not only is David dead, and his body "corrupted" or decayed, Peter and his audience know where David's tomb is (Acts 2:29).David was a prophet, as many of his psalms prove. And he knew that God promised he would have an heir who would reign over Israel forever (2 Samuel 7:16). So, David saw that this heir would die, but would rise again; he would not stay in the place of the dead—not even long enough for his body to decay. These are very specific qualifications that have only been fulfilled in one person: Jesus (Acts 2:32).
Peter uses the word "Christ" which is the Greek translation of the Hebrew word mashiyach, which we translate "Messiah." Jesus' disciples understood Him to be the Messiah (Mark 8:27–29), but they were very confused about what the Messiah was. They knew the Messiah was the promised one of Isaiah 9:1–7, whom they believed would free Israel from Roman rule and usher in a time of great peace and prosperity. They didn't understand He was also the suffering servant of Isaiah 53 who had to die for the sins of the world. Even in the very last moments before Jesus ascended into heaven, the disciples thought He would take control of the nation (Acts 1:6). It wasn't until they received the Holy Spirit (Acts 2:1–4) that they understood that, for now, His kingdom is in the hearts of His people (John 18:36).