LDS Definition: Jesus Christ taught that baptism is essential to the salvation of all who have lived on earth (see John 3:5). Many people, however, have died without being baptized. Others were baptized without proper authority.
Because God is merciful, He has prepared a way for all people to receive the blessings of baptism. By performing proxy baptisms in behalf of those who have died, Church members offer these blessings to deceased ancestors. Individuals can then choose to accept or reject what has been done in their behalf.
Some LDS have wondered what critics, particularly mainstream Christians, say regarding Paul's scripture discussing baptism for the dead. Here is one christian's comments from 'The Cross Unveiled to Mormons':
1 Corinthians 15:29 “Else what shall they do which are baptized for the dead, if the dead rise not at all? why are they then baptized for the dead?”
This is the only reference to the kind of this practice in the Bible so it is extremely important to understand the context so doctrines are firmly built on biblical principles. For this verse it is imperative to read what Paul had been talking about before verse 29 so we can understand what he is saying and why he is saying it. Reading from verse 12 you see that Paul is speaking to people who do not believe in the resurrection, yet have introduced a ritual of baptisms for the dead. Paul informs them that if there is no resurrection of the dead then Christ is not risen, and if Christ is not risen then his preaching and your faith is in vain and we are still in our sins.
He then tells them in verse 29 that if you don't believe in the resurrection why are you baptizing for the dead? Paul argues that what is the point of your practice of this ritual because there is nothing to be gained from it. This point is extremely clear because Paul is not including himself in the context because he says “they” and not “we”. This verse, being the only one that mentions this practice, is something that Paul is obviously condemning. This verse does not teach the doctrine of baptism for the dead the way Mormons interpret it and there is no other mention of this practice in the bible. If it were meant to be a doctrine practiced, it would have been made clear by the apostles. Interpretation of verses to determine doctrine must be built on the majority and not the minority.
Reference: Link is here.