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Salvation for the dead
From MormonWikiDoctrine and Covenants is the account of a vision received by President Joseph F. Smith, and it helps explain principles of salvation for the dead.
In his opening address at the eighty-ninth Semiannual General Conference of the Church, on October 4, 1918, President Smith declared that he had received several divine communications during the previous months. One of these, concerning the Savior’s visit to the spirits of the dead while His body was in the tomb, had been received the previous day. It was recorded immediately following the close of the conference; on October 31, 1918, it was submitted to the counselors in the First Presidency, the Quorum of the Twelve Apostles, and the Patriarch, and it was unanimously accepted by them as scripture.
(for the full text: Section 138)
1–10, President Joseph F. Smith ponders upon the writings of Peter and our Lord’s visit to the spirit world; 11–24, He sees the righteous dead assembled in paradise and Christ’s ministry among them; 25–37, How the preaching of the gospel was organized among the spirits; 38–52, President Smith sees Adam, Eve, and many of the holy prophets in the spirit world who considered their spirit state before their resurrection as a bondage; 53–60, The righteous dead of this day continue their labors in the world of spirits.
The basic, eternal questions that befuddle mankind are the following: Who am I? Why am I here? Where am I going? The Plan of Salvation revealed by the prophets answers the first two questions satisfactorily, but the third is better understood after reading Doctrine and Covenants, section 138. When men die, they suffer a physical death, which is a separation of the spirit from the body. While the body is discarded, the spirit lives on, and it moves to one of two realms—spirit prison, or spirit paradise—two divisions of the Spirit World. This is a division between the wicked and the righteous. Upon the resurrection of Jesus Christ, the righteous spirits in paradise who died before Christ's resurrection were also resurrected. "And [they] came out of the graves after his resurrection, and went into the holy city, and appeared unto many (Matthew 27:53)." Another resurrection will take place at His Second Coming, and another after the millennium.
In the spirit world, all men and women have the opportunity to hear the gospel of Christ and can either accept or reject it. However, spirits can not perform their own ordinances. Those must be performed by beings with physical bodies. Hence the reason why Latter-day Saints perform sacred ordinances for their deceased ancestors. These ordinances can be accepted or rejected by spirits in the spirit world, as they will.