The only reference in scripture to the Second Anointing is found in Doctrine and Covenants 124:28, a revelation by Joseph Smith, Jr commanding the building of a temple in Nauvoo, Illinois, in part, because "there is not a place found on earth that he may come to and restore again that which was lost unto you, or which he hath taken away, even the fulness of the priesthood.") (emphasis added).
The Second Anointing differs from the "first anointing", which is part of the Endowment ceremony, in that where the first anointing promises blessings in the afterlife contingent on the patron's faithfulness, the Second Anointing actually bestows those blessings. According to prominent Twentieth Century Latter-day Saint Apostle Bruce R. McConkie, those who receive the Second Anointing "receive the more sure word of prophecy, which means that the Lord seals their exaltation upon them while they are yet in this life. . . . [T]heir exaltation is assured." McConkie at 109-10.
The Second Anointing was given to women as well as men, and some have argued that because women received the Second Anointing, and thus were anointed queens and priestesses, and ordained to the "fulness of the priesthood", there is a good argument that Smith considered them to have, in fact, received the Priesthood power (though not necessarily a specific Priesthood office). See Quinn, Women and Authority: Re-emerging Mormon Feminism.
The Second Anointing in the Church of Jesus Christ of Latter-day Saints
Unlike many other Mormon ordinances such as baptism, most members of the Church of Jesus Christ of Latter-day Saints do not consider the Second Anointing to be essential for salvation. However, Joseph Fielding Smith, acting as Church Historian and Apostle, stated, "There is no exaltation in the kingdom of God without the fulness of the priesthood." (In Bruce R. McConkie, Doctrines of Salvation: Sermons and Writings of Joseph Fielding Smith 3:132 (Salt Lake City: Bookcraft, 1956).)