Christian religion co-opted him and made him a companion to St Nicholas. St Nicholas is NOT Santa. St Nic leaves candy and treats to good children on St Nicolas Eve (not Christmas) and Krampus dealt with the naughty ones. He would beat them with sticks, wrap them in chains and carry off the EXTRA naughty ones in a basket on his back.
He is a very Germanic character and the German cultural issues today of raising proper well behaved children still use Krampus as a threat.