Physical death is the separation of the spirit from the mortal body. The Fall of Adam brought physical death into the world (see Moses 6:48). Because of the Atonement and Resurrection of Jesus Christ, all mankind will be resurrected and redeemed from physical death.
Death is an essential part of Heavenly Father's plan of salvation (see 2 Nephi 9:6). In order to become like our Eternal Father, we must experience death and later receive perfect, resurrected bodies.
When the physical body dies, the spirit continues to live. In the spirit world, the spirits of the righteous "are received into a state of happiness, which is called paradise, a state of rest, a state of peace, where they shall rest from all their troubles and from all care, and sorrow" (Alma 40:12). A place called spirit prison is reserved for "those who [have] died in their sins, without a knowledge of the truth, or in transgression, having rejected the prophets" (D&C 138:32). The spirits in prison are "taught faith in God, repentance from sin, vicarious baptism for the remission of sins, the gift of the Holy Ghost by the laying on of hands, and all other principles of the gospel that [are] necessary for them to know" (D&C 138:33-34). If they accept the principles of the gospel, repent of their sins, and accept ordinances performed in their behalf in temples, they will be welcomed into paradise.
Because of the Atonement and Resurrection of Jesus Christ, physical death is only temporary: "As in Adam all die, even so in Christ shall all be made alive" (1 Corinthians 15:22). Everyone will be resurrected, meaning that every person's spirit will be reunited with his or her body—"restored to their proper and perfect frame" and no longer subject to death (Alma 40:23; see also Alma 11:44-45).