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From MormonWikiSons of Perdition, who are not redeemed by the Atonement of Jesus Christ.
Satan and his followers are beings of spirit who were denied bodies and cast out of heaven during pre-mortal existence (see Plan of Salvation). After the millennium, after the last great battle between the forces of God and the forces of Satan, Satan and his followers will be cast into Outer Darkness.
The Sons of Perdition are those who have lived as mortal men and women on the earth, have had the heavens opened to them and received a certain knowledge that Jesus is the Christ, and then have rejected the Savior, "having denied the Only Begotten Son of the Father, having crucified him unto themselves and put him to an open shame" (Doctrine and Covenants 76:34-35; see also Doctrine and Covenants 76:31–33, 36–37). These men and women cannot be redeemed, and will be the only ones who will suffer the second death. The first death is physical death, and everyone but the devil and his angels will overcome physical death through Resurrection. The second death is spiritual and is separation from God. Everyone but the Sons of Perdition and the devil and his devils, will overcome spiritual death through the Atonement of Jesus Christ. However, sons of perdition cannot achieve forgiveness and will be completely cast outside of the light of God. Hence, the term outer darkness. They will not have access to the Holy Ghost or Heavenly Father or Jesus. In short, Outer Darkness is eternal torture. Another name for Outer Darkness is hell.