What does 1 Corinthians 11:1 mean?

Scripture was originally written without chapter and verse divisions. Those were added many centuries later, to make it easier for readers to locate specific passages. In some cases, those traditional boundaries are questionable, at best. In this case, verse 1 is best understood to conclude Paul's teaching in chapter 10, more so than to begin a new thought in chapter 11.

In the previous verse, 1 Corinthians 10:33, Paul described his practice of setting aside his personal freedoms and rights and preferences in order to please everyone in everything he does. Paul did not mean that pleasing other people was his ultimate goal. Rather, he has a responsibility to remove anything possible from his own personal practice that might trip someone up on their way to faith in Christ. Of course, Paul would not set aside his convictions about Christ or his practices of prayer and preaching, for instance. Beyond those core elements of his faith, however, he was willing to set aside anything he had a right to do in order to lead as many people as possible to faith in Christ.

Now he concludes that thought by calling the Corinthians to follow his pattern for living just as he follows Jesus' pattern for living. Jesus also set aside living for His own advantage while on earth, including refusing to demand His right to be recognized and honored as the Son of God (Philippians 2:6). Paul followed Christ's example and urged his readers to follow his own.