What does 1 Corinthians 16:10 mean?

Paul is wrapping up his long letter to the Corinthians with a few closing business matters. He has instructed them about how to collect money for a special contribution, as well as detailing his travel plans for coming to see them in person once again.

Paul does not plan to travel to see them directly, but he will be sending Timothy to them. Timothy's role may be both to deliver this letter and represent Paul among them. Paul had previously mentioned that Timothy was coming to them in 1 Corinthians 4:17, "That is why I sent you Timothy, my beloved and faithful child in the Lord, to remind you of my ways in Christ."

Paul had mentored Timothy in ministry ever since meeting the younger man while on a missionary journey that took him through Lystra in Asia Minor (Acts 16:1). Timothy joined Paul's team at that point and had become one of Paul's most-loved and trusted disciples. Timothy eventually became the pastor of the church at Ephesus.

Timothy's mention here is because he was with Paul during his time in Corinth, so he knew the people there. Paul now tells them to treat Timothy well by "[putting] him at ease." Perhaps Paul expects there to be a confrontation over the things he has written in his letter to them. He knows some in Corinth oppose him. He has noted deep division among the people (1 Corinthians 1:10–11). His letter has challenged them regarding their sex lives, style and manner of worship, and in their relationships with each other.

He reminds the Corinthians that both he and Timothy are doing the work of the Lord among them. In other words, Paul's teaching is from Christ, not from himself or Timothy.