What does Galatians 2:13 mean?

Paul continues to relate a story about confronting Peter, as a way of emphasizing both his legitimate authority and the importance of faith—not works—in salvation.

Peter was in Antioch, visiting the Christians there. Antioch wasn't like Jerusalem. It was a big town with far fewer Jewish people. Peter had apparently gone along with the local customs, and sat down to eat at a table with non-Jewish people. Based on his background, that was no small thing. Peter had grown up in a Jewish culture being faithful to follow the Law and Jewish customs. He had learned early on that is what made him a good person. Jesus had changed all of that. Peter agreed that because of Jesus' death and resurrection, it was not necessary for Gentiles to live as Jews under the Law in order to be saved.

In fact, it was not necessary for Jews to live under the Law, either, but it would be hard for the faithful Jews to stop doing so. For one thing, it had always been forbidden to eat at a table with Gentiles. When a group of men who believed it was still wrong walked in while Peter was eating, he jumped up to move away from the Gentiles. Peter was clearly afraid of what those men would think of him, that they would judge him. Peter was also a leader, though, so his choice led all of the other Jewish people at his table—including even Barnabas, Paul's partner—to leave the table, as well.

It was an ugly moment, and Paul calls it what is was: hypocrisy. Peter said he believed that the Gentiles were fully accepted by God's grace through faith in Christ, but he didn't want to get caught acting like that was true. He showed that, in that moment, he cared more about what people thought of him than he did about pleasing God.