What does Acts 21:16 mean?

Paul is on the 64-mile journey from Caesarea Maritima to Jerusalem along with Luke, Sopater, Aristarchus, Secundus, Gaius, Timothy, Tychicus, and Trophimus (Acts 20:4), as well as a contingent from Philip's church in Caesarea. It's unclear if Mnason lives in Jerusalem or somewhere along the way.

This is the end of Paul's third missionary journey, which is the last recorded in the book of Acts. He will reach Jerusalem and report to James and the elders of the church. They will rejoice over the establishment of the church in Ephesus as well as the news Paul brings of the faithfulness of the churches in Troas, Philippi, Thessalonica, Berea, and Corinth. But they bear troubling news, as well. A rumor has spread that Paul is teaching Jewish Christians they no longer have to follow the Mosaic law. To prove them wrong, Paul agrees to help a group of men complete their Nazirite vow. Before they can finish the ceremony, however, another rumor flies that he has brought a Gentile—Trophimus—into the temple. The issue escalates quickly and results in Paul being under house arrest for five years (Acts 21:17–36).

Even as Paul faces these challenges, the Holy Spirit surrounds him with support. Some of his traveling companions have been with him for years, others for months. Those from Caesarea accompany him because they're concerned about him. Staying with Mnason—who apparently has followed Jesus since that first Pentecost or even earlier—must be more comforting than staying in an inn. Soon, Paul will be back in Caesarea—under house arrest but able to visit with the church members (Acts 24:23). And Luke and Aristarchus will travel with him to Rome (Acts 27:2).

Initially, when the Holy Spirit warned Paul's friends that he would be arrested, they thought they were supposed to prevent him from going to Jerusalem. Soon, they learn the Holy Spirit is preparing them to support Paul.