Baptism for the Dead
Billions of people have lived on this earth who have never learned about Jesus Christ. They knew nothing about His commandments, His ministry, or His atonement. Mormon doctrine (The Church of Jesus Christ of Latter-day Saints) teaches that men cannot be saved in ignorance. Neither can they be condemned in ignorance.
When people die, their spirits separate from their bodies, and they go to a place called the Spirit World to await resurrection and judgment. In the spirit world, we can enjoy our loved ones who have already passed on, but we can also learn, for there we have agency (the freedom to choose), just as we had on earth. During the three days that Jesus was in the tomb, He organized a ministry in the Spirit World, so that those who had never heard it could be taught His gospel. (Read about it here.)
When Christ was on the earth, serving among men, He was baptized. Although He was the only sinless person ever to live on the earth, He underwent baptism by immersion “to fulfill all righteousness.” Baptism by the proper authority is the gate to heaven and salvation.
However, baptism can only be performed in mortality, because it takes a body to do it. Those who have died without the ordinance would never be able to achieve baptism. Those in the Spirit World who accept the gospel of Jesus Christ there, however, do have the opportunity to be baptized by proxy, in the temples of God on earth.
Mormons do this work in their temples in a room called a baptistery. The baptistery is located in the basement of each temple. It is below ground, because baptism by immersion represents the death of the old creature and one’s rebirth in Christ. It also represents the death and resurrection of the Savior. The baptismal font is designed after the laver in the temple of King Solomon in ancient Israel. It is symbolically mounted on the backs of twelve oxen, standing for the twelve tribes of Israel.
Members of The Church of Jesus Christ of Latter-day Saints are fully engaged in family history work to find the names of their deceased ancestors and provide baptism for them. Mormon genealogy work blesses the lives of many thousands of people of other faiths in many ways. The main Family History Library in Salt Lake City houses millions of records available to anyone who is interested in their own family history. The Church’s online database has millions of names accessible to anyone. Local family history centers in various Mormon meetinghouses are also available to the public, and volunteers there help anyone who asks. Mormons also volunteer to index records from assorted databases worldwide, making them available digitally. Millions of records have been digitalized in this way, including those of Ellis Island in New York, through which millions of immigrants have entered the United States.
LDS News on Church policy for proxy baptisms