It's not an ignorant question. You've touched on something that has great value to Latter-day Saints. Not only has the LDS Church partnered with Ancestry.com and others to make their genealogical records available to church members and developed FamilySearch to organize and collaborate family history research, the LDS Church also has the world's largest collection of genealogical records archived in a huge vault in granite mountains.
The Church of Jesus Christ of Latter-day Saints' three-fold mission is:
First, to proclaim the gospel of the Lord Jesus Christ to every nation, kindred, tongue, and people;
Secondly, to perfect the Saints by preparing them to receive the ordinances of the gospel and by instruction and discipline to gain exaltation;
Thirdly, to redeem the dead by performing vicarious ordinances of the gospel for those who have lived on the earth. (See Ensign, May 1981, p. 5.)
Or more succinctly:
proclaim the gospel, to perfect the Saints, and to redeem the dead.
Although "the three-fold mission" is not as frequently recited these days, these three primary values remain paramount in LDS living. As such, great efforts are made and sacred tithing funds are expended to share the gospel and to help both the living and the dead follow the example of Christ and receive essential ordinances.
In The Family: A Proclamation to the World, it states:
The divine plan of happiness enables family relationships to be perpetuated beyond the grave. Sacred ordinances and covenants available in holy temples make it possible for individuals to return to the presence of God and for families to be united eternally.
Pretty much everything Mormons do revolves around strengthening families in Christ, and since in LDS theology the family unit can extend beyond the grave, knowing who your ancestors are and which ordinances they have received is really important.
The Old Testament promises us the spirit of Elijah (in Malachi 4):
5 Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the Lord:
6 And he shall turn the heart of the fathers to the children, and the heart of the children to their fathers, lest I come and smite the earth with a curse.
It is probably because of this promise that it is not uncommon for people to report spiritual experiences as they research their family history and cultivate a stronger connection with their past.
The importance of genealogy is reinforced several times in the scriptures. Jesus' literal and royal lineages are both recorded in the New Testament. Several lineages are reported in the Old Testament, and The Book of Mormon has many others.
Knowing lineages allows Latter-day Saints to perform ordinances for their deceased ancestors in temples if they had not received them while living. Even though everyone is saved from death by Christ's resurrection, without the necessary ordinances we cannot live in God's presence with our family and become like He is. Thus, genealogy becomes vital in helping our families receive the ordinances of the gospel (like baptism).
Because Mormons believe that all of us are children of God, knowing who has gone before us helps us better understand our eternal identity and purpose. As we connect generations in the gospel, we better understand our relationship to God and come closer to Him.