What does 1 Corinthians 16:18 mean?

Coming to the end of his letter, Paul has been praising Stephanas and his household to the rest of the Christians in Corinth. Stephanas and two other men, perhaps servants from his household, came to visit Paul in Ephesus. Most likely, these men brought the letter Paul has been responding to in this epistle (1 Corinthians 7:1). He may have sent what we now know as 1 Corinthians back with these three men.

In the previous verse, Paul wrote that their arrival has made up for the absence of the Corinthians. By this, he seems to have meant that he has been missing his friends in Corinth and these men helped him feel better about that. Now he adds that they refreshed his spirit. They have truly been encouraging to him.

Paul has urged the Corinthians in verse 16 to put themselves under the authority of servant-leaders such as Stephanas and now he commands them to give recognition to such people. Clearly, Paul cared deeply for Stephanas. It's also possible that Stephanas represented those among the Corinthians on the correct right side of the doctrines Paul had written about in this letter. If so, Paul may be telling the others to side with Stephanas on those issues.