What does Acts 16:14 mean?

Normally, when entering a new city, Paul attends the local synagogue and waits for an opportunity to speak (Acts 13:5, 14; 14:1; 18:4). He explains how Jesus of Nazareth fulfilled the Messianic prophecies of the Old Testament and how He died and rose again for the forgiveness of sins (Acts 13:16–41). Some of the Jews and God-worshiping Gentiles accept his claim, while others don't (Acts 13:43; 17:4). Philippi, however, doesn't seem to have the requisite ten Jews needed to maintain a synagogue. All it has is a group of women who worship the Jewish God and meet on the Sabbath at the river to pray.

One of these is Lydia. Thyatira is a town in Asia. The "Asia" mentioned here is not the modern continent, but a large province which takes up the western third of modern-day Asia Minor. Thyatira is one of the seven churches mentioned in Revelation. Jesus warns them against a woman in their congregation who entices members into a mystery sex cult, although He also recognizes a good number in the church follows Him well (Revelation 2:18–29). We don't know if Lydia returns to Thyatira and is part of this church; if she is, she is almost certainly not the idolatrous woman.

That Lydia sells purple goods, native to her district, infers that she is wealthy. She soon invites Paul, Silas, Timothy, and Luke to stay in her home, which proves she is also generous. The church that starts with Lydia and her household continues that generous tradition, supporting Paul in his ministry to Thessalonica (Philippians 4:15–16).

Ironically, Paul had wanted to plant churches in Asia. There are many sizeable cities with strong Jewish populations that would welcome, to some degree, the message of Jesus. The Holy Spirit herds him away, however, to an Asian woman on the border of Macedonia and Greece.