Elizabeth is a witch. She was in the witch coven that brought Donna back to life. The circle was looking for a sixth member of their coven so they wanted Donna. Donna's life was saved by them so she would be forever in their debt. To bring back Donna to life they needed a sacrifice. So they killed the spirit of a girl, who would not return. The girl was completely destroyed and didn't had a chance to get an afterlife.
Elizabeth seems to be the leader of the coven. She tells the other witches what they have to do.