Assuming that “fathers” refers to the patriarchs, and “children” refers to the later Israelites, the turning of the hearts would speak of the reconciliation that would occur between the patriarchs and the later Israelites. When Jesus ministered on earth, he addressed this disharmony between the patriarchs and the Israelites of his day. The Jews of Christ’s day claimed that Abraham was their father. Yet Christ said, “If you were Abraham's children, you would be doing the works Abraham did, but now you seek to kill me, a man who has told you the truth that I heard from God. This is not what Abraham did” (John 8:39). There was no harmony between Abraham and his children of Christ’s day. Abraham looked forward in faith to the seed that would be born of his descendants, through whom all the nations of the world would be blessed. But the Jews of Christ day hated the Promised Seed, Jesus Christ.
Furthermore, there was no harmony between the patriarch Moses and the Jews of Christ’s day. The Jews said to the blind man (whom Jesus had healed), "You are [Jesus’] disciple, but we are disciples of Moses” (John 9:28). But on an earlier occasion, Jesus had said to the Jews that Moses would accuse them before the Father on the day of judgment (John 5:45). There was no agreement, no harmony between the Jews of Christ’s day and Moses.
What God promises is that the coming Elijah would be instrumental in bringing about a reformation in the church, so that there would be harmony between the patriarchs (who served God faithfully) and their later descendants (who did not serve God faithfully).
Of course, this turning of hearts of fathers to children, and vice versa, also implies that there would be a return to the Lord. The point of disagreement between the generations revolves around the love for, and the obedience to, the Lord.
6 And he will turn the hearts of fathers to their children and the hearts of children to their fathers, lest I come and strike the land with a decree of utter destruction.”