What does Acts 11:21 mean?

Devout Jews, living on Cyprus and in Cyrene, and familiar with the Greek culture and language, had learned about Jesus in Jerusalem (Acts 2). When Saul persecuted the church in Jerusalem, they fled and shared Jesus' story as they travelled (Acts 8:1–4). Some of these Jesus-followers were from the island of Cyprus and the city of Cyrene in Libya. They traveled north, to Syrian Antioch, and didn't just share Jesus in the synagogues like others; they shared Jesus with Gentiles. God blessed their efforts, and many of the Gentiles came to a saving faith in Jesus.

In Acts 10, Peter learned that Jesus had come for the Gentiles as well as the Jews. Earlier in Acts 11, Peter explained this truth to the church in Jerusalem; some of the more legalistic Jewish Jesus-followers still had a difficult time accepting it. The Jews who regularly interacted with Gentiles had much less resistance to the idea. They see no reason why their friends wouldn't be interested in Jesus and even less doubt that Jesus is interested in their friends. They're right.

The wording here can be awkward when parsed into English. This does not imply some people can believe but not turn to the Lord. Alternative phrasings are, "a large number of these, believing, turned to the Lord," or, as the NIV says, "a great number of people believed and turned to the Lord."