Galatians 2:11-12,16 (NKJV)
Now when Peter had come to Antioch, I withstood him to his face, because he was to be blamed; for before certain men came from James, he would eat with the Gentiles; but when they came, he withdrew and separated himself, fearing those who were of the circumcision.
... knowing that a man is not justified by the works of the law but by faith in Jesus Christ, even we have believed in Christ Jesus, that we might be justified by faith in Christ and not by the works of the law; for by the works of the law no flesh shall be justified.
Are you shocked? Peter, the great apostle of our Lord Jesus Christ, a hypocrite? And this after he had been filled with the Holy Spirit and full of power? Paul had to set him straight. Peter was doing just fine, eating ham sandwiches with the gentile Christians, until some of his Jewish buddies come to town and Peter changed his tune. I can relate to this, been there, done that...ashamed of it too. Being an influential and important man, Peter's behavior affects others too.
What's the point? Aside from the fact that even leaders need correction, the main reason Paul brings up this incident is to make it clear that the only way we can be saved is by faith in Jesus Christ. Jews are not saved by the law and so neither can Gentiles be saved by the law.
What does this say about Peter and Paul's relationship? For one, it is clear that when it comes to truth, anyone standing on the side of truth has authority over anyone who is in error. This account does not give us Peter's response but I imagine he felt convicted right way and repented of his sin. If their relationship was ever strained, it certainly was later restored. When Peter wrote his last epistle, he had this to say about Paul:
2 Peter 3:15 (NIV)
Bear in mind that our Lord's patience means salvation, just as our dear brother Paul also wrote you with the wisdom that God gave him.