What does 1 Corinthians 5:3 mean?
A man in the Corinthian church is known to be carrying on an affair with his father's wife. Incest of this kind was not tolerated either by the Jewish followers of the law or by Roman society, yet the Corinthian Christians had allowed it to continue among them without addressing it.Paul has written that they must act. First, they should mourn over this man's sin among them. One of their own is harming himself and others by living in ongoing sexual immorality instead of following the way of Jesus. In addition, they must immediately remove the man from their meetings.
This is not just a suggestion. Paul claims his authority as an apostle of Christ Jesus. He declares his spiritual presence with them—through this letter and their unity together in the Christ. It's not entirely clear if Paul means to say that he is also present with them in some additional supernatural sense through the power of the Holy Spirit.
In either case, Paul insists that he is present enough with them to declare this man guilty and command that he be removed from his place among the other Christians. Apparently, there was no question about whether this man was sleeping with his father's wife. Everyone knew it, and Paul used his authority to pass judgment on the man. His rationale will be explained in the following verses: the goal is to restore the man's spiritual health.