What does Acts 11:4 mean?

Peter is the most noted of Jesus' twelve disciples. He seems to be responsible for the largest number of Jesus-followers in Jerusalem (Acts 2). He is not the pastor of the church in Jerusalem, but he holds a lot of authority. But he and the members of the Jerusalem church are also Jews. That is, they practice the same tenets of Judaism which they've always held. They see Jesus as the Jewish Messiah, and they consider Jesus' teaching, sacrifice, and resurrection to be the fulfillment of the promises of Judaism.

This is why the Holy Spirit had to give Peter an elaborate vision and a direct order before he would go with three strangers to the home of a Gentile (Acts 10:9–20). Under the traditions and rules which grew from Old Testament laws, Jews do not mix with Gentiles. They do not visit them or have close friendships, and they especially don't eat with them. Peter did follow the Holy Spirit's leading. He entered the home of a Roman centurion and found a houseful of attentive listeners. Because of Peter's obedience, those Gentiles accepted Jesus as their Savior and received the Holy Spirit.

When Peter returned to Jerusalem, the legalistic Jewish Jesus-followers, called "the circumcision party," were critical (Acts 11:2). The "circumcision party" did right by directly addressing their concerns (Acts 11:3). Peter did better by graciously explaining (1 Peter 3:15–16). Both sides valued unity enough to listen to each other. That commitment to unity led to a resolved conflict (Acts 11:18).

Like Peter, here, our actions should be honorable and Spirit-led enough that a straightforward explanation is all it takes to clear things up. And we should be open to the Spirit's leading and admit when we're wrong.