This is a curious verse as it does not easily fit into the Pauline (or overall Biblical) understanding of baptism. The first question that arises is why are the Corinthians baptizing for the dead? The second question here is does Paul approve of the action?
As one might imagine the answers to these questions are complicated. There are a variety of answers for the first the first question, none may be satisfactory. The most likely answer is this: the Corinthian people hold baptism in high esteem. This is a result of their understanding that baptism is required to enter into the Kingdom of God. This high view of baptism can be seen in 1 Cor. 1:13-17. There seems to be a desire of the Corinthians to guarantee the save passage to the Kingdom through baptism, even after death, of their loved ones (one can imagine this happening within a family or household unit). They are wrong in their practice, but not in their intentions. There is also know indication that this practice was common among all of the Corinthians church. The Greek (no need to get too deep into the details on this) suggests that this was a small number of people, not a large one.
As to Paul’s acceptance of the practice, we must remember two things. First, just because there is an absence of Paul’s critique of the practice doesn’t mean that Paul is accepting of it. It is just a matter of fact, even for a small group. Second, Paul’s silence could suggest that he sees no need to critique the practice. All are fully aware and understand that it is not consistent with new “Christian” practices. This is the only place in the whole of Scripture where the practice is mentioned. Further, there is no place in Scripture where it is done. Paul just may assume that the rest of the Corinthians have been taught that the practice was aberrant.