We know very little about what Elijah did to turn the hearts of the fathers (in the spirit world) to the children (still on earth). What we know is what has transpired on this side of the veil—that the spirit of Elijah has spread over the entire earth. The hearts of the children have turned to the fathers in a way so miraculous that it could only be the work of God. The August 2000 Ensign tells us how fast this spirit is spreading, “The Church’s FamilySearchä Internet Genealogy Service, a source of 640 million names worldwide, received its three billionth hit in May, just under a year after the site was introduced…The Pedigree Resource File…is growing at the rate of 1.1 million names a month as users submit personal family records via www.familysearch.org.” (Ensign, Aug. 2000, p. 79) These are only a couple of indices of a work that has exploded since Apr. 3, 1836.
Boyd K. Packer
"The spirit of Elijah spoken of by the Prophet here and on other occasions is something very real. When a member of the Church comes under its influence, it is a powerful, compelling force which motivates him with a desire to be attending to genealogical and temple work. It leaves him anxious over the well-being of his forebears. When that spirit comes, somehow we desire to know more about those forebears-we desire to know them.
“If we can literally be ‘caught up’ in any work in the church, it is this work relating to genealogical research and to the temples. This, because there is the spirit of Elijah. The prophets have spoken of it. The Saints have felt it; and following the inspiration of it they have come to the temple to do the sacred work for both the living and the dead.” (The Holy Temple, p. 210)
Joseph Smith explained that it is not enough for the hearts of the children to turn to the fathers unless there is some binding force to tie them for eternity to their ancestors:
"Now, the word turn here should be translated 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 sealing 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 of the Prophet Joseph Smith, p. 330)
James E. Faust
“Perhaps we regard the power bestowed by Elijah as something associated only with formal ordinances performed in sacred places. But these ordinances become dynamic and productive of good only as they reveal themselves in our daily lives. Malachi said that the power of Elijah would turn the hearts of the fathers and the children to each other. The heart is the seat of the emotions and a conduit for revelation. This sealing power thus reveals itself in family relationships, in attributes and virtues developed in a nurturing environment, and in loving service. These are the cords that bind families together, and the priesthood advances their development.” (Ensign, May 1993, p. 37 as taken from Latter-day Commentary on the Book of Mormon compiled by K. Douglas Bassett, p. 456)