Our interest comes for two reasons. The first is not singular to the LDS church; in fact, if you came upon this page on purpose, you're afflicted too. I refer to the Genealogy Bug. For the last two centuries, people all over the world have suddenly become interested in their ancestry. I don't need to go into detail as to why--you probably know just as well as I do.
The second reason is due to a fundamental teaching of the Latter-day Saints. We believe families are forever. We believe the love and friendship developed within the family unit on earth can be preserved eternally. We believe a man and woman, married by the proper authority and in the proper place, can live together for time and for all eternity. We believe that man and that woman will be able to have and to hold their children as they do in this life.
Yes, we believe in an after-life; a life where we can be with our loved ones. In fact, we can be with our children, our grandchildren, our parents, our grandparents, and our great-grandparents all the way back to Adam. We can meet great-uncles and aunts whom we never had the priviledge of knowing in this life. We can talk with our great-great-grandparents who crossed the Atlantic to the New World or who faught in the Crusades (on one side or the other). We can hold our great-great-great-grandchildren and be held by our great-great-great-grandparents.
This knowledge fills me with an excitement I can barely contain. Knowing I will actually meet them someday gives me all the reason I need to find out who my ancestors are; however, there is more to it than simple curiosity. Because my ancesters have already left this earth, they are not able to be married for eternity ("sealed") by those who have the authority to do so. However, I can do it for them! In a special ceremony, a worthy person may stand in the place of his or her ancester and be sealed on behalf of that ancester. This sealing may be to a spouse, a parent, or a child. By doing this, we can ensure all of our family will have the opportunity to be part of our eternal family.
About now, somebody might be wondering what happens if the ancester doesn't want this work done for him or her. Well, the answer is simple--nothing happens. This work for the dead, as we call it, is done simply to give them a choice; if they don't want to accept it, they don't have to. That is how God's whole plan works--He gives choices to His children and then leaves the making of the choice up to them.