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John the Baptist baptizes Jesus Christ in the River Jordan. (Matthew 3:13-17)
In the waters of baptism, we make sacred covenants with the Lord. We promise to be His disciples, and to take upon us the name of Christ. In many Christian religions, baptism is essential to salvation. In Mormonism this is true as well. The Church of Jesus Christ of Latter-day Saints has a great doctrine and understanding of the principle.
Jesus Christ, the one who was perfect, without sin, needed baptism for His own salvation. Many like to focus on the aspect of baptism where it washes away our sins, making us clean. Why would the sinless Christ have need of such a thing? But it does more than just cleanse sins.  Baptism is the first step in a series of covenants that we must make in order to live with God once more. It numbers us with those on the Lord's side, and our willingness to do so allows us to show the Father we are humble enough to submit to His will. This is why even Jesus had need to be baptized. He did so to submit to the will of the Father, and to lead us by example in the direction we must go. If even the perfect Jesus Christ has need to be baptized by water, how much greater need do we have to do the same?
Some Christian denominations, Mormonism among them, stress the importance of baptism by immersion, meaning that the individual being baptized must go all the way under the water. Some may wonder why this aspect of baptism is so important. The reason a person must be immersed is that, at its core, baptism symbolizes quite plainly the death, burial and resurrection of Christ. The baptizee "dies" and is "buried" in the water. They are then "resurrected", being pulled back out of the water a new person. It signifies the end of  a life of sinning, and rebirth as a disciple of Christ. In the LDS Church, no other way is sufficient. All those wanting to live with their Heavenly Father once more must partake in baptism by the proper authority.
Being mortal, we are weak. We have temptations and opportunity for sin all around us. It is inevitable that each of us will slip from time to time, and many of these slip-ups take place after baptism. After we have been completely cleaned, we become dirty once more, and no unclean thing can dwell with God. For this, our Father in Heaven has provided us with a wonderful gift: the Sacrament. In Mormonism, Church meetings take place every Sunday. In one of these meetings, those practicing repentance can renew their baptismal covenants by taking the sacrament: broken bread and water which has been blessed by the proper priesthood authority. This special meeting imitates Jesus Christ's "Last Supper", in which he blessed bread and wine and gave of it to His disciples, asking them to partake in remembrance of Him. The wonderful gift of the Sacrament allows us to re-cleanse ourselves, becoming just as clean as we were at baptism.
Do little children need baptism? No. Jesus has proclaimed that little children are alive in Christ. They are completely perfect and incapable of sin, because they don't know any better. Little children who die are not accountable and so are guaranteed salvation. The LDS Church therefore, only baptizes those who are over the age of eight. 
But what about those who die without baptism, who would have accepted the Gospel of Jesus Christ if only given the chance?  They are not out of luck. This is one purpose of Mormon Temples; the redemption of the dead. Faithful Latter-day Saints may be baptized in place of their ancestors, allowing the deceased to choose if they accept this ordinance on their behalf. Thus, all who have sufficient faith may partake in baptism. What a wonderful feeling it is to enter the waters of baptism and to become purified in Christ.
For more info on the Sacrament, click here.