Elijah came to restore to the earth, by conferring on mortal prophets duly commissioned of the Lord, the fulness of the power of Priesthood. This Priesthood holds the keys of binding and sealing on earth and in heaven of all the ordinances and principles pertaining to the salvation of man, that they may thus become valid in the celestial kingdom of God. …
It is by virtue of this authority that ordinances are performed in the temples for both the living and the dead. It is the power which unites for eternity husbands and wives when they enter into marriage according to the eternal plan. It is the authority by which parents obtain the claim of parenthood concerning their children through all eternity and not only for time, which makes eternal the family in the Kingdom of God.
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.
Excerpts taken from Teachings of Presidents of the Church: Joseph Fielding Smith, Chapter 17, Sealing Power and Temple Blessings.