What does Acts 15:24 mean?
The church in Syrian Antioch had been the first to see a significant number of Gentiles come to a saving relationship with Jesus. When the church in Jerusalem heard, they sent Barnabas to investigate. Barnabas found that their faith was true, but they needed teaching. So, he sent to nearby Tarsus and brought over Paul to help (Acts 11:19–26). Once the church was well-established, Paul and Barnabas traveled to the island of Cyprus and up through central modern-day Asia Minor, planting churches that also included a mix of Gentiles and Jews (Acts 13—14). They then returned and reported their success.Not too long after, Jewish Christians from the sect of the Pharisees arrive from Judea. Despite recognizing Jesus as the Jewish Messiah, they have a difficult time fully embracing the truth that Jesus provides salvation from sins through grace alone, not by obedience to the law they so love. In addition, they know if they socialize with Gentiles in the church, they will lose their social standing as Pharisees (Matthew 23:5–7; Galatians 6:12). They soon fight against the church, insisting that Gentiles must be circumcised and follow the Mosaic law—convert to Judaism—before they can follow the Jewish Messiah (Acts 15:1). The Pharisees are more concerned about their reputation than the fact their actions are "distort[ing] the gospel of Christ" (Galatians 1:7).
Paul, Barnabas, and a contingent from Antioch take the issue to the church in Jerusalem who agree with them, despite the interference of more Pharisees. Now, the council writes a letter to send back to Antioch and the churches Paul and Barnabas planted (Acts 15:2–23).
"Some persons" are the Pharisaical Jews. In other places, they are referred to as "the circumcision party" (Acts 11:2; Galatians 2:12; Titus 1:10) or "Judaizers." They so harass Paul and Barnabas' church plants in Galatia that Paul declares he wishes they would go all the way and emasculate themselves (Galatians 5:12).
The wording, "gone out from us," could indicate these are the same people Paul mentions in Galatians 2:11–14. In that event, Peter was visiting the church in Antioch when the Pharisees arrived and so shamed the Jews that Peter and Barnabas stopped eating with the Gentile Christians. Paul publicly corrected them. Paul identified the Pharisees as "certain men [who] came from James," meaning James, the half-brother of Jesus and pastor of the church in Jerusalem.
It isn't clear if the Jerusalem church is disavowing "some persons" or if they're disavowing some of what they said. Either way, they fully endorse the messengers Paul, Barnabas, Judas, and Silas (Acts 15:25, 27).