From Church History and Modern Revelation, 2:332:
The Lord has placed the baptismal font in our temples below the foundation, or the surface of the earth. This is symbolical, since the dead are in their graves, and we are working for the dead when we are baptized for them. Moreover, baptism is also symbolical of death and the resurrection, in fact, is virtually a resurrection from the life of sin, or from spiritual death, to the life of spiritual life. (See D. & C. 29:41–45.) Therefore when the dead have had this ordinance performed in their behalf they are considered to have been brought back into the presence of God, just as this doctrine is applied to the living.From Smith, Doctrines of Salvation, 2:323–27:
The symbolism of baptism applies also to the living. When we are baptized, it is as though we are buried and resurrected with Christ. Our old, sinful natures die and we become a new person (see Romans 6:1–7). Baptism also symbolizes the physical process of being born, so that when we emerge from the waters, it is as though we have been born a second time (see John 3:5; Moses 6:59–60). For further discussion of the symbolism of baptism.Again from Doctrines of Salvation,2:121–22:
If Elijah had not come, we are led to believe that all the work of past ages would have been of little avail, for the Lord said the whole earth, under such conditions, would be utterly wasted at his coming. Therefore his mission was of vast importance to the world. It is not the question of baptism for the dead alone, but also the sealing of parents and children to parents, so that there should be a ‘whole and complete and perfect union, and welding together of dispensations, and keys, and powers, and glories,’ from the beginning down to the end of time.
If this sealing power were not on the earth, then confusion would reign and disorder would take the place of order in that day when the Lord shall come, and, of course, this could not be, for all things are governed and controlled by perfect law in the kingdom of God.
Why would the earth be wasted? Simply because if there is not a welding link between the fathers and the children—which is the work for the dead—then we will all stand rejected; the whole work of God will fail and be utterly wasted. Such a condition, of course, shall not be.Quoted in The Utah Genealogical and Historical Magazine, Volumes 12-13, Idaho Falls Genealogical Convention, April, 1922.
My brethren and sisters, keep in mind this thing; that as was expressed yesterday, we without our dead cannot receive the fulness of salvation. We must understand that those who have died without a knowledge of the Gospel are just as much entitled to receive the privileges of salvation as are we who are living now when the Gospel is restored. And the Lord has arranged it so that they shall not be overlooked, but that every soul shall have the opportunity of salvation. And in order that the family chain shall not be broken it becomes necessary for us to perform labors for our dead, and ward workers must keep these things constantly in mind and give them to the people in their visits among them.Joseph Fielding Smith, "The Keys of the Priesthood Restored," Utah Genealogical and Historical Magazine, July 1936, 100-101.
I think sometimes we look at this work for the salvation of the dead rather narrowly. It is a wrong conception to think of the people for whom we are doing work in the temple of the Lord as being dead. We should think of them as living: and the living proxy but represents them in receiving the blessings which they should have received and would have received in this life had they been living in a gospel dispensation. Therefore every dead person for whom work is done in the temple is considered to be living at the time the ordinance is given.Quoted in Hearts Turned to the Fathers: A History of the Genealogical Society of Utah, 1894-1994 (1995), 184.
It doesn't matter whether your computer is able to compile all the family group sheets for everyone that every lived on the earth, it remains the responsibility of each individual to know his kindred dead... Even if the work is done, then it is still each person's responsibility to study and become acquainted with his ancestors.See Sealing Power and Salvation, Brigham Young University Speeches of the Year (January 12, 1971) 2-3. Italics removed.
The doctrine of salvation for the dead is one of the most glorious principles ever revealed to man. It is the way in which the gospel shall be offered to all men. It establishes the fact that God is no respecter of persons [see Acts 10:34] that every soul is precious in His sight; and that all men will, in fact and in reality, be judged according to their works.
Now, I thank the Lord that He has restored His everlasting gospel to us in this day. I thank Him for the sealing power returned to earth by the Prophet Elijah, I thank Him for the eternal family unit, for the privilege we have of being sealed ourselves in his holy temples, and for then making available these sealing blessings to be given to our ancestors who died without a knowledge of the gospel.