What does Acts 16:3 mean?

Paul had just witnessed a major council in Jerusalem. This resulted in Peter and James, the leaders of the church, condemning any thought that Gentiles must be circumcised to follow the Jewish Messiah (Acts 15:1–21). Paul and Silas are traveling with the letter (Acts 16:4) explaining that the only requirements to be placed on Gentile believers was that they "abstain from what has been sacrificed to idols, and from blood, and from what has been strangled, and from sexual immorality" (Acts 15:29). These are moderate requirements or reminders, meant to make Jewish believers feel comfortable sharing meals with their Gentile brothers in the faith. In addition, Paul's letter to the people here, in the district of Galatia, states that if Gentiles get circumcised because they think following the Mosaic law will save them, then Jesus is worthless to them (Galatians 5:2–6). He goes so far as to say those who teach such things should just castrate themselves (Galatians 5:12).

Yet, now, Paul takes Timothy, a resident of Galatia, and circumcises him. The difference here is in motivation: Timothy is Jewish since Jewish ethnicity passes through the mother (Acts 16:1). Paul senses the young man will have a major role in the church, and he doesn't want to give legalistic Jewish Christians any reason to find fault in him. If Timothy is not circumcised, the Jewish Christians might see it as a stumbling block to their faith (Romans 14:13). It's about ministry, here, not salvation, and Paul knows that sacrifice is necessary for the spread of the gospel (1 Corinthians 9:12, 19, 23; Colossians 1:24).

Timothy will go on with Paul as his "true child in the faith" (1 Timothy 1:2). Paul will continue the spiritual and personal training Eunice and Lois, Timothy's mother and grandmother (2 Timothy 1:5; 3:14–15), started. Timothy will represent Paul to several churches (1 Corinthians 4:17; Philippians 2:19) and eventually pastor in Ephesus (1 Timothy 1:3).