The Krampus is a middle European (mainly Austria, Germany, parts of South-Italy and Croatia, as well as sometimes Hungary) type of frightening creature, who accompanies Nikolaus (the original "Santa Claus", Nikolaus von Myra).
The name originates from the Austrian dialect word for lifeless, dried up or faded, or the old-German word for claw.
A typical Austrian tradition is the so called "Krampus-Lauf" (Krampus-Run) on the 5th or 6th of December (depending on the region), where townspeople dress up in furs and with devilish masks (wearing tails and horns). They accompany Saint Nikolaus who will give presents to the good children, while the Krampuses will punish the naughty children (often by hitting them with their birch [a birchwood rod]). Krampuses will also carry buckets or bags made out of fur, in which - so it is said - they will carry away the very naughty children. This tradition originally had nothing to do with Christmas, but was a Pagan tradition assimilated by the church in the 17th century (therefore, Saint Nikolaus is dressed up like a bishop).