Their hope is in your hands

"Many of your deceased ancestors will have received a testimony that the message of the missionaries is true. When you received that testimony you could ask the missionaries for baptism. But those who are in the spirit world cannot. The ordinances you so cherish are offered only in this world. Someone in this world must go to a holy temple and accept the covenants on behalf of the person in the spirit world. That is why we are under obligation to find the names of our ancestors and ensure that they are offered by us what they cannot receive there without our help....

"[The Savior] has trusted you by letting you hear the gospel in your lifetime, giving you the chance to accept the obligation to offer it to those of your ancestors who did not have your priceless opportunity. Think of the gratitude He has for those who pay the price in work and faith to find the names of their ancestors and who love them and Him enough to offer them eternal life in families, the greatest of all the gifts of God. He offered them an infinite sacrifice. He will love and appreciate those who paid whatever price they could to allow their ancestors to choose His offer of eternal life....

"You are not just gathering names. Those you never met in life will become friends you love. Your heart will be bound to theirs forever...

"After you find the first few generations, the road will become more difficult. The price will become greater. As you go back in time, the records become less complete. As others of your family search out ancestors, you will discover that the ancestor you find has already been offered the full blessings of the temple. Then you will have a difficult and important choice to make. You will be tempted to stop and leave the hard work of finding to others who are more expert or to another time in your life. But you will also feel a tug on your heart to go on in the work, hard as it will be.

"As you decide, remember that the names which will be so difficult to find are of real people to whom you owe your existence in this world and whom you will meet again in the spirit world. When you were baptized, your ancestors looked down on you with hope. Perhaps after centuries, they rejoiced to see one of their descendants make a covenant to find them and to offer them freedom. In your reunion, you will see in their eyes either gratitude or terrible disappointment. Their hearts are bound to you. Their hope is in your hands. You will have more than your own strength as you choose to labor on to find them."

- Elder Henry B. Eyring, Of the Quorum of the Twelve Apostles, "Hearts Bound Together," Ensign, May 2005, p. 78-80
http://www.lds.org/ensign/2005/05/hearts-bound-together?lang=eng