Great response A train
LDS believe the often quoted statement by Paul: 'For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.' (Romans 6:23)
Without much deeper definition of sin itself, let it suffice to consider all actions in transgression of the laws of God as such.
We believe that the salvation through the atonement of Jesus the Messiah, which is the gift of God, is infinite, eternal, and not only is potent to save man from death, but sin itself also. For 'ye cannot be saved in your sins' (Alma 11:37), but we believe in salvation from sin.
As you may know, we believe in The Book of Mormon which is a record of an ancient American people who had prophets of the God of Israel among them. Alma and Amulek were two such prophets who lived around 70 to 80 B.C.
In The Book of Mormon in the eleventh through the thirteenth chapters of the Book of Alma, Alma and Amulek engage in a public discussion with one Zeezrom, a cunning lawyer who denied the Messiah and even offered to pay the prophets to deny the existance of any Supreme Being. (Alma 11:2)
In the discussion that followed sin and death were defined by the prophets in a plain and informative manner. While I would say that you should read these three chapters (which aren't that long), I will summarize some key points of interest.
First, there are two deaths. The first death is the physical, temporal death which is ever familiar to all of mankind as the dissolution of our mortal body. The second death is a spiritual death, which is the seperation of us from God, or death 'as to things pertaining unto righteousness.' (Alma 12:16)
We believe that the work of Christ as the Propitiator of our sins is designed to bring mankind, who is subject to both physical death and seperation from God through sin, back to a oneness with God, therefore this work is called the At-one-ment of Jesus Christ. The Atonement is designed to save us from such separation, making us at one with God.
The power of Christ's resurrection is universal as stated by Amulek: 'this restoration shall come to all, both old and young, both bond and free, both male and female, both the wicked and the righteous; and even there shall not so much as a hair of their heads be lost; but every thing shall be restored to its perfect frame, as it is now, or in the body, and shall be brought and be arraigned before the bar of Christ the Son, and God the Father, and the Holy Spirit, which is one Eternal God, to be judged according to their works, whether they be good or whether they be evil.' (Alma 11:44)
John the Revelator saw both the resurrection and the judgement saying: 'I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.' (Rev. 20:12)
LDS look forward to the literal resurrection of all mankind regardless of the belief or lack thereof on the part of individuals to be so raised. But as John continued: 'And death and hell were cast into the lake of fire. This is the second death. And whosoever was not found written in the book of life was cast into the lake of fire.' (Rev. 20:14-15)
As symbolized by a 'lake of fire', the eternal separation from God issued to those 'not found written in the book of life' is the Second Death. For as Alma said: 'God did call on men, in the name of his Son, (this being the plan of redemption which was laid) saying: If ye will repent and harden not your hearts, then will I have mercy upon you, through mine Only Begotten Son; Therefore, whosoever repenteth, and hardeneth not his heart, he shall have claim on mercy through mine Only Begotten Son, unto a remission of his sins; and these shall enter into my rest. And whosoever will harden his heart and will do iniquity, behold, I swear in my wrath that he shall not enter into my rest.' (Alma 12:33-35)
'We believe that through the Atonement of Christ, all mankind may be saved, by obedience to the laws and ordinances of the Gospel.' and 'that the first principles and ordinances of the Gospel are: first, Faith in the Lord Jesus Christ; second, Repentance; third, Baptism by immersion for the remission of sins; fourth, Laying on of hands for the gift of the Holy Ghost.' (Articles of Faith 3 and 4)
The question you have raised has devoted to it many volumes. I hope this is a little start in the right direction.