What does Acts 23:33 mean?

Paul is back in Caesarea Maritima. He had arrived there after his third missionary journey and continued to Jerusalem where he knew he would be arrested (Acts 21:8–15). While in Jerusalem, he learned someone had been spreading the rumor that he taught Jews they didn't have to circumcise their sons. The leaders of the church in Jerusalem asked him to fulfill a Jewish ceremony to show his fealty. While doing so, Jews from modern-day Turkey accused him of bringing a Gentile into the temple. They incited the crowd to beat him until the Roman tribune rescued him by arresting him (Acts 21:17–35). The tribune Lysias tried to find out what Paul had done by allowing the Sanhedrin to question him, but Paul managed to start a fight between the Pharisees and Sadducees, instead (Acts 23:1–10). The next day, Paul's nephew overheard forty Jews conspiring with the Sanhedrin to assassinate Paul. The tribune gave up and sent Paul to the governor in Caesarea (Acts 23:16–24).

The tribune knows Paul is a Roman citizen (Acts 22:27) so he does what he can to keep Paul safe. He sends two centurions, two hundred soldiers, seventy horsemen, and two hundred spearmen to escort Paul (Acts 23:23). When they reach Antipatris, roughly halfway, the infantry and spearmen return to Jerusalem and the horsemen continue (Acts 23:31–32).

The letter is Lysias' explanation to the governor Felix. In it, he gives a summary of the previous few days—conveniently leaving out the part where he didn't find out Paul was a Roman citizen until he had bound him and nearly flogged him, both of which were illegal to do without a trial and conviction (Acts 22:24–29). Lysias also warns Felix that Paul's accusers are on their way for the trial (Acts 23:26–30).