This is a hard-to-understand verse. This is the best and most comprehensive response I have found for it on the web:
Baptism for the Dead?
“Otherwise, what will they do who are baptized for the dead, if the dead do not rise at all? Why then are they baptized for the dead?”
The most notorious interpretation of 1 Corinthians 15:29 is the one advocated by Mormonism—that people who are alive on the Earth can be baptized, and the efficacy of that baptism then is offered to those who already have died and are in the spirit realm. But this verse cannot be teaching proxy baptism as practiced by the Mormons. Many other passages eliminate that possibility by stressing the singular necessity of responding obediently to God in this life (e.g., Proverbs 11:7; John 8:24; Luke 16:26; 2 Corinthians 5:10; Hebrews 9:27). The Mormon view is in direct contradiction to what the Bible teaches from beginning to end. We have only this life in which to make our decisions, and when we leave this life, we have no further opportunities to repent (Luke 16:25-31; Hebrews 9:27).
At least four adequate explanations exist that avoid contradicting the rest of the Bible. First, “dead” refers to the “old man of sin” (Romans 6:6). We are baptized for the dead in the sense that we are baptized in water to eliminate the dead man of sin. Hence Paul was asking why one would be baptized to eliminate the old man of sin in anticipation of eternal acceptance if the resurrection will not be forthcoming.
Second, “dead” refers to the world of lost souls—those who are spiritually dead. “They” refers to the apostles and “baptism” refers to the baptism of suffering that the apostles endured in order to make known the Gospel to the world (alluded to in passages like Mark 10:38-39, Luke 12:50, Acts 9:16, and 1 Corinthians 4:9). Thus Paul was asking why the apostles would subject themselves to the baptism of suffering, in behalf of the spiritually dead people of the world if, in fact, no one has hope of the resurrection.
Third, “they” refers to those who are baptized in water on the basis of the preaching and teaching done by those who had since died. In other words, why would a person obey the command to be baptized, and thereby have hope of life beyond the grave, if the one who taught the person to be baptized has since died and will not be raised from the dead?
Fourth, Paul was using the logical argument form known as argumentum ad hominem—an argument based upon what men were doing at that time and with which the readers would be familiar. The Corinthians were familiar with people who practiced an immersion for the benefit of the dead. He used the third person pronoun “they” as opposed to “you” or “we.” New Testament baptism would have been referred to in the first or second person. This tactic of referring to what outsiders were doing (without implying endorsement) to make a valid spiritual point was used by Paul on other occasions (e.g., Acts 17:28; Titus 1:12).
These four possible interpretations each have contextual evidence to support them. None of the four contradicts any other Bible doctrine. What is critically important is that we not miss Paul’s point in 1 Corinthians 15. He brought up the subject of baptism for the dead for one reason: to reaffirm the reality of the resurrection. Christians were being drawn into the destructive heresy that the general resurrection is fictitious. In a setting where he ardently defended the actuality and centricity of the resurrection, he advanced two questions. If the resurrection and end-time events are not to occur, then “why are they baptized for the dead?” and “why do the apostles stand in jeopardy every hour?” (vss. 29-30). He wanted the Corinthians to face the fact that many things Christians do have meaning only if resurrection is an anticipated and ultimate objective. If when we die, that’s it—no future conscious existence—why take risks living the Christian life as the apostles frequently did? If this life is all there is, forget Christianity and live it up (vs. 32)! But resurrection is coming! So do not live this life indulging the flesh and mingling with those who will influence you to do so (vs. 33). Live righteously, and get your mind straight in view of your knowledge of the coming resurrection (vs. 34).