What does Acts 21:15 mean?

Paul, Luke, and a group of men from Macedonia and modern-day Turkey (Acts 20:4) are on the last stretch to Jerusalem. They landed in Tyre, stayed a week, spent one day in Ptolemais, and have been in Caesarea Maritima since. A few of the church members from Caesarea accompany them.

Luke and the other companions are probably bringing donations their churches gathered for the church in Jerusalem (Romans 15:26). The church members from Caesarea go to introduce them to Mnason with whom they will stay (Acts 21:16). Paul is going knowing full well the Roman soldiers will imprison him.

Paul has known his fate for several months. However, it's only recently that he has convinced his friends it is the Holy Spirit's will (Act 20:22–24; 21:13–14). It's natural for people to see the drawbacks of Jesus' chosen apostle to the Gentiles being locked up. But for the next two years, at least, it won't be as bad as they fear. In Jerusalem, Paul will be beaten and arrested, but he will avoid being flogged and murdered (Acts 21:33; 22:24–29; 23:12–24). For his protection, the Roman tribune will send him back to Caesarea where he will share Jesus' story with Herod Agrippa II, and the church in Caesarea will be able to visit and minister to him as much as he needs (Acts 24:23; 26). Even when Paul faces the long, hazardous sea voyage to Rome, Luke and Aristarchus are with him (Acts 27:2). And when he reaches the end, he will be in Rome, chained to Roman guards who will take his message to Caesar's household while a steady stream of visitors come to hear about Jesus (Acts 28:16, 30–31; Philippians 4:22). In addition, he will write Ephesians, Colossians, and Philippians.

Paul proves faithful to God and God proves faithful to His people.