In Mormonism, a "son of perdition" is a person who has achieved complete clarity and understanding that God exists and then has subsequently rejected that truth. The person can reject this truth by either performing an act of murder or expressing approval of the crucifixion of Jesus Christ.
In either case, once this person has performed one of these acts, he becomes a son of perdition. Mormons believe that it is extremely difficult to become a son of perdition, as a complete understanding of the truth of God can only arise from a direct message from heaven, and only then can a person choose to not except the message as truth.
The Church of Jesus Christ of Latter-day Saints often uses the term "perdition" as the proper name for Satan or Cain. Perdition in this context means "destroyer" or "destruction." Therefore, those who choose to follow Satan are called the sons of perdition. This group also includes Satan's followers, who are said to have been cast out of heaven when they followed Satan in his rebellion against God.
Mormon scripture states that during the final judgement day, those who have been deemed sons of perdition have to live out the rest of their existence in a realm called "the outer darkness" under the rule of Satan and Cain.