Krampus is a Hardmode, post-Planteraenemy that appears during the Frost Moonevent. Its first appearance in the event is on Wave 8. Defeating a Krampus does not reward any points during the Frost Moon, as of version 126.96.36.199; before that version, it awarded 10 points.
Krampus is known in Alpine folklore as the evil version of Santa Claus (or a companion of Saint Nicholas), punishing or capturing children who misbehave during the Christmas season.
The Bestiary entry for the Krampus: "Every year, Krampus is tasked to punish all of the naughty children, but he's taken the day off to participate in this mayhem instead!"