Think of the Grinch with a really, really bad temper and you are getting close.
Krampus is an incubus who accompanies Santa Claus, but does not follow the old man’s prerogative of present giving. An incubus is a demon in male form which visits sleepers and lies upon them (the word comes from the Latin ‘incubo’ which is to lie on top).
The Krampus is not your common or garden night rapist, however: his brief is to punish the children who have misbehaved during the year. In early twentieth century postcards, you can see the whip (or Virgacs) he would carry with him
trying to find a place to buy garcinia (which is right here anyway.)