Generally speaking, then, we are prone to think of the coming of Elijah as essential to the great genealogical (family history) work which results in temple work for the dead. But there is more, as Elder McConkie (above) suggested, and this pertains to the living. In Moroni’s words, because Elijah came, the hearts of the children (we who now live in mortality) turn to the fathers (Abraham, Isaac, and Jacob—see D&C 27:10; D&C 98:32). That is to say, because Elijah came to earth and restored the keys of sealing and also the fulness of the blessings of the priesthood, there comes into our hearts a desire to have all of the blessings of the ancient fathers—the blessings of the gospel, the priesthood, and eternal life (Abraham 2:8-11). There is only one place on earth wherein those blessings may be obtained, and that is in temples of the Lord, through the ordinance of celestial marriage. We then want the same for our children. And, by extension, we want all of those same blessings for our more immediate fathers, and thus the need for genealogical research and temple work for the dead.
“And He Shall Turn the Heart of the Fathers to the Children, and the Heart of the Children to Their Fathers”
Moroni used the phrase “plant in the hearts of the children the promises made to the fathers.”
The Prophet Joseph clarified this by saying that the words turn or plant could be translated as bind or seal.
“But what is the object of this important mission? or how is it to be fulfilled? The keys are to be delivered, the spirit of Elijah is to come, the Gospel to be established, the Saints of God gathered, Zion built up, and the Saints to come up as saviors on Mount Zion.
“But how are they to become saviors on Mount Zion? By building their temples, erecting their baptismal fonts, and going forth and receiving all the ordinances, baptisms, confirmations, washings, anointings, ordinations, and scaling powers upon their heads, in behalf of all their progenitors who are dead, and redeem them that they may come forth in the first resurrection and be exalted to thrones of glory with them; and herein is the chain that binds the hearts of the fathers to the children, and the children to the fathers, which fulfills the mission of Elijah.”
(Teachings, p. 330.)