Jesus Christ lived, suffered pain and anguish, and died for our sins. He suffered so that we would not have to, and through Christ every single person is saved from physical death in the Resurrection. Christ's "death bringeth to pass the resurrection, and redeemeth all mankind from the first death -- that spiritual death; for all mankind, by the fall of Adam being cut off from the presence of the Lord, are considered as dead, both as to things temporal and to things spiritual. But behold, the resurrection of Christ redeemeth mankind, yea, even all mankind, and bringeth them back into the presence of the Lord." (Helaman 14:16-17). So, even though all people are affected by the Fall of Adam, Christ covered it completely for us out of love. Not only this, but all people will be brought before God and Jesus Christ for a chance to be judged.
The Atonement was done for all people, and "if ye shall believe on His name ye will repent of all your sins, that thereby ye may have a remission of them through His merits" (Helaman 14:13). We are saved completely by the grace of Jesus Christ, not by our own actions, good works, or efforts. But, it is still vital that we repent and serve God and Christ to show our love and obedience to them. As I've been told, grace is provided for all, but the "door" to grace is faith, good works, and repentance. Christ provides redemption for all, but He would never take away our free will to choose it or not. It is up to us to use our free agency and decide that we want it, and then to "open the door". Christ has faith in us and our capability to love and serve Him obediently; why shouldn't we reciprocate our faith and love back to Him?