Krampus (Full Name: Hector Krampus) is the shadow of Santa Claus who punishes misbehaved children on Christmas and in this case, he is the bigger bad and true main antagonist of Scott Cawthon's Five Nights at Freddy's game franchise. He was the one that raised The Purple Man to kill those children in the first place all along.
During the production of the cartoon series named Fredbear and Friends on December 12th 1983, they were surrounded by Krampus' helpers and were forced to run the show with only one season. But after years of torment and torture (even after the show ended), the creators of the show died at the hands of the Christmas demon himself. As Krampus ran away to his place, he found a purple-skinned crying and decided to raise him as his own. Over the years, he taught his unholy child how to become a killer and murderer. And after those years, Krampus' child who was now The Purple Man, was ready to do his father's work. Since then, Krampus grew more powerful to punish any children that stands in his way.
Corrupting the Company
On December 1st 1986, he spread his dark magic to Fazbear Incorporated with the aid of his helpers. That's when the company shutdown with The Purple Man aiding his father. This also happened to be secured when Kramps bit Fitzgerald's head violently back in The Bite of 87. And since the arrival of Mike Schmidt and the unnamed security guard at Fazbear's Fright, he has successfully fulfilled his purpose: spread darkness to those near him or to those that encounter him.
Resurrecting the Company
It was Christmas Eve on 2017 (30 years after The Bite of 87) and the Comapny was resurrected by the help of the CEO of the company: none-other than Mike Schmidt himself. Krampus got furious and decided to go on a vengeful rampage on those that stopped him and recently encountered Freddy, Bonnie, Chica, and Foxy, including their toy incarnations amongst others (Balloon Boy, Marionette, etc).
When he was face to face with Mike, the sun of Christmas morning rose and went to hide in the darkness. Meaning that he no longer can punish those around him. So it means that he will come back once again to punish those around him, even after Christmas.