What does Acts 16:2 mean?

Paul and Silas are in Galatia, the district in central modern-day Asia Minor, encouraging the churches Paul had planted with Barnabas. Part of that encouragement is letting the Gentile Jesus-followers know that, despite the insistence of Jewish Christian Pharisees, they do not have to be circumcised (Acts 15). While in Lystra, the two meet a young man named Timothy. His mother is Jewish, and his father is Greek (Acts 16:1). He's well respected by his fellow believers, something which factors into his growing leadership role in the church (1 Timothy 4:12–16).

The district of Galatia is named after the 10,000 Gallic mercenaries and their families who were invited to stay by Nicomedes in the first century BC. During Paul's first trip to Iconium, he and Barnabas managed to plant a church, but the unbelieving Jews riled up the Gentiles and the city leaders. When Paul and Barnabas heard they were planning on stoning them, they fled to Lystra (Acts 14:1–7).

Lystra was a market town about a day from the main road. The town was a Roman colony settled by Augustus' Roman veterans, and the townspeople spoke more Latin than Greek. The first time Paul was there, the people had confused him with Hermes and Barnabas with Zeus; they then tried to offer sacrifices to them. Shortly after Paul and Barnabas convinced them to stop, the people were convinced by Jews from Pisidian Antioch and Iconium to stone Paul and leave him for dead (Acts 14:8–23).

Knowing that the churches in Lystra and Iconium are doing well would have been a great encouragement to Paul. Encountering Timothy, Paul's "true child in the faith" (1 Timothy 1:2), is even better.