The Curse of Thorn is placed on a child by the cult leader. It commands that child to kill his entire family as a blood sacrifice to keep the cult alive. It also makes that child able to withstand serious injuries that would result in death for any normal human being. It turns the child into pure evil.
The Curse of Thorn was placed on Michael Myers by Dr. Wynn in 1963. He succeeded in killing his sister Judith Myers, and later his neice, Jamie Lloyd. By this time Jamie's baby, Stephen, was the only remaining member of Michael's bloodline, and once he was made the final sacrifice, Wynn intended to pass the Curse of Thorn onto Danny Strode. However, Michael killed all the cult members before he had the chance. It is unknown of the Curse of Thorn eventually wore off with Wynn's presumed death, or if it was permanent until his bloodline was severed.
Dr. Loomis implies in Halloween 5: The Revenge of Michael Myers that once Michael completed his task he would be destroyed by the rage inside him. This is touched upon in the fan film The Last Halloween (The Death of Michael Myers), when precisely that happens.
The nature of the Curse of Thorn is never revealed until Halloween: The Curse of Michael Myers.