Paul's first appeal in 1 Corinthians is concerning the discord that he has heard about in the church at Corinth. Paul says that some in Corinth are saying that they are "of Paul" while others are saying that they are "of Apollos" or "of Peter". We can guess from the rest of the content of the letter that these divisions are connected to the spiritual arrogance of the Corinthians. (Consider the divisions Paul addresses concerning the Lord's Supper and spiritual gifts later in the letter). It seems likely that they are each claiming the leader they see as being the most spiritual. The really spiritual, of course, say that they are "of Christ".
Paul will address these themes as they touch other problems throughout the letter but he begins here by asking the Corinthians three questions that are meant to remind them that they have been bound together in Christ. Is Christ divided? Was Paul crucified on your behalf? Or were you baptized into the name of Paul? Each question reinforces the others. Christ is not something that can be divided up among a few believers. Instead, it was Christ who crucified on behalf of all the Corinthians. Therefore, all the Corinthians have been baptized into Christ. That is to say that Christ is not something to which any of them can lay claim over and against the others. Instead, their lives, their identities are defined by their baptism into Christ and this is an identity that all the Corinthians share.
Of course, the Church today still divides itself and thus divides Christ in this way as well. We say we are "of Luther" or "of Calvin" or "of Wesley" while others claim to be the only ones who are truly "of Christ". Then there are all the other labels that threaten to divide us as well: black, white, Hispanic, rich, poor, educated, old, young, and every other label the world gives us or we give ourselves. Paul reminds us that in Christ there is more that unites us than divides us. That doesn't meant that we all have to become the same but it does mean that as the Church we must demonstrate a unity of love with one another even in the midst of our diversity.
It is telling that Paul begins this passage on unity by addressing the Corinthians as brothers. This simple address in its own subtle way is also a reminder to the Corinthians of their common bond together. They are brothers because they have the same Father. It is this Father who has bound the Corinthians together by the crucifixion of his Son and the empowering of his Holy Spirit.