"I appeal to you, brothers, in the name of our Lord Jesus Christ, that all of you agree with one another so that there may be no divisions among you and that you may be perfectly united in mind and thought." NIV translation
Divisions had started among the believers at Corinth and Paul urges them to put aside those and stay united in Christ. We are called, as believers, to be a part of the body of Christ and so we should be focused on Christ and unified in our faith in Him.
"My brothers, some from Chloe's household have informed me that there are quarrels among you. What I mean is this: One of you says, 'I follow Paul'; another, 'I follow Apollos'; another, 'I follow Cephas'; still another, I follow Christ.'" NIV translation
The believers in Corinth were confused and becoming divided because they started following a teacher instead of the teaching. A teacher is to simply proclaim the Word of the Lord using the talent and wisdom that God has provided. God may use one person to speak to a certain group of people and another to speak to a different group.
It seems that even more today, people get caught up with the method instead of the message but we must remember that it is all about sharing the gospel of Jesus Christ. Speakers may come and go but the Word of God will stand forever.
"Is Christ divided? Was Paul crucified for you? Were you baptized into the name of Paul?" NIV translation
Paul asks some ridiculous questions in order to get them to see how these quarrels are just nonsense. The obvious answers to them are no! These divisions are just as big if not even bigger today. It seems that many people elevate the teacher to a place that is above the Word and that, my friends, is not right.
"I am thankful that I did not baptize any of you except for Crispus and Gaius, so no one can say that you were baptized into my name. (Yes, I also baptized the household of Stephanas, beyond that, I don't remember if I baptized anyone else.)" NIV translation
Paul always kept things about Jesus and he even goes so far as to be thankful that he did not baptize many people. He always wanted to point them to Jesus and instead many were trying to elevate a man to the place of Christ (the head of the church).