Samhain was the Celtic God of the Harvest worshipped by the Druids, he was a demon who became associated with the holiday Halloween due to it's ties with the original Celtic/Druid ceremony. He became trapped in a loop, no longer worshipped, he simply waited, until Halloween, each year gaining more power, each year being defeated by the Ghostbusters. His ultimate desire to envelop the world in eternal darkness, or as he sometimes now says, a Halloween that will never end.
Samhain eventually created a new foothold in our world, a son, named Samuel Hain.
Though the full extent of his power is unknown, it is very clear he has a weakness to sunlight.