Son of perdition is a phrase used in The Church of Jesus Christ of Latter-day Saints (LDS Church) and by Mormon fundamentalists to describe a person who will not take part in the glory of God in the afterlife. This is in contrast to the vast majority of people, who will receive a "kingdom of glory" after the Final Judgment, and enter into one of three degrees of glory after the resurrection: Celestial, Terrestrial, or Telestial Kingdoms.
Most Latter-day Saints believe that the sons of perdition will be cast into outer darkness; the scriptures do not use this exact phrase in connection with the sons of perdition, but state that they "shall go away into the lake of fire and brimstone, with the devil and his angels."
Mormons believe that free will is one of the greatest gifts of God, and that there might be some who will completely reject Jesus Christ and salvation. God will not force someone, including Satan, to be saved if they do not desire to be saved. Therefore, the Sons of Perdition are allowed to remove themselves from the presence of God and live in whatever degree of darkness they desire.
They are “different” (unbiblical) on just about every front. And it makes me sad because some of the sweetest people I’ve known were Mormons. I have some LDS cousins and I just cannot imagine how they went from the strong Christian faith of our great grandparents to such quackery. That aside, like most sincere false religionists they are going about to establish their own righteousness. They don’t understand that “...Christ Jesus, who of God is made unto us wisdom, and righteousness, and sanctification, and redemption.” They don’t know that for those in Christ, HE is our righteousness.