What does 1 Corinthians 1:16 mean?

Paul is making an aside from his main point that no Christian is legitimately baptized in the name of some teacher, preacher, or apostle. They are baptized in the name of Jesus, and all their loyalty and focus should be on Him. Instead, the believers in Corinth had divided into factions based on their loyalty to well-known Christian teachers.

Paul wrote in verse 14 that the only ones among them he had baptized were Crispus and Gaius. Now he recalls that he also baptized the household of Stephanas and allows that he may have baptized more people he is not remembering while he was with them in Corinth.

His point, though, remains that it does not matter whom he did or did not baptize because nobody was baptized in his name. All Christians are baptized in the name of Jesus. Further, this continues to emphasize that baptism is not part of our salvation. Paul's concern is the gospel, not a good work such as being baptized.