What does Acts 3:13 mean?
Peter has just healed a lame man in the temple (Acts 3:1–9). When the man starts leaping, the people recognize him and realize what has happened. They mob Peter and John, and Peter explains the power that healed the man did not come from them but from Jesus (Acts 3:10–12). The man was healed by faith in the name of Jesus (Acts 3:16) whom God raised (Acts 3:15) and glorified.Peter gives a short summary of the crucifixion and the people's part in it in Acts 3:13–15. The Sanhedrin arrested Jesus because of jealousy (Matthew 27:18). But they had limited authority to execute a criminal (John 18:31)—plus, they didn't want backlash for killing Jesus, whom the people considered a prophet (Mark 14:1–2). The Sanhedrin brought Jesus to Pilate, the Roman governor, but Pilate didn't want anything to do with the case. After Pilate questioned Jesus, he wanted to release Him, so he had Jesus flogged and humiliated, hoping it would be enough to satiate the Sanhedrin's wrath. But the Jewish leaders told Pilate that releasing Jesus was rebellion against Caesar. Pilate didn't want the Sanhedrin to riot against him any more than the Sanhedrin wanted the people to riot against them, so Pilate agreed to have Him crucified (John 18:28—19:16).
The sequence of events shows how culpable the Jews are in the death of Jesus. Although the Jewish leadership was the driving force, to the point of inciting the crowd to their cause (Matthew 27:20), God dealt with the Jews in a more collective way. Even if some in Peter's audience weren't there in Jerusalem at the time of the crucifixion, they carried the guilt of their people.
That same collective identity is why Peter describes God as the God of the Jewish patriarchs. Today, nearly two thousand years later, we tend to think of Christianity divorced from Judaism, or replacing it. In the early days of the church, Christianity was well understood to be a fulfillment of Judaism. The same God who took the Jews for His people brought them Jesus. The same prophets who contributed to the identity of the Jews foretold Jesus' coming (Acts 3:21–25). When presenting the good news to the Jews, the apostles start with the Jewish Scriptures. If they reject Jesus, they reject their own faith.