What does Acts 13:28 mean?

The Jews and the God-fearing Gentiles of the synagogue in Pisidian Antioch would try to travel to Jerusalem for one or more of the three major festivals: Passover, Pentecost, and the Feast of Tabernacles (Deuteronomy 16:16). But it would be difficult for anyone—even if they lived in Judea—to attend all three feasts every year; it was impossible for someone who lived so far away from Jerusalem. Even though these men know about John the Baptist, they may not know anything about Jesus of Nazareth, His crucifixion, and the rumors of His resurrection. Before Paul can explain how Jesus fits within the context of God's saving work in Israel's history, he must explain who Jesus is.

"They" are the Sanhedrin: the Jewish ruling council composed of priests, scribes and elders, primarily from the party of the Sadducees, but also including some Pharisees. They had many reasons for wanting to kill Jesus. He broke their human-imposed Sabbath laws (Mark 3:1–6), gained too much popularity (Matthew 27:18), and embarrassed them in front of the crowds (Mark 12:13–40). But they had no capital offense with which to charge Him. So, they hired men to lie about Him. This didn't work, because the false witnesses couldn't synchronize their stories. Finally, they got Him to say He was the Son of God (Mark 14:57–63).

Pilate, the governor of Judea, knew the Sanhedrin had no legitimate charges, but he didn't want the Jewish leaders to start a riot or accuse him of treason against Caesar. To keep the peace Pilate agreed to crucify an innocent man (John 18:28–32; 19:6–16).