What do they find out about the Witch? What is she actually?

The White Witch has crowned herself Queen of Narnia, but is frightened by the prophecy that her reign, as well as her life, will end when two Sons of Adam and two Daughters of Eve assume the four thrones at Cair Paravel. The White Witch is descended from Lilith, the original companion created for Adam, before Eve and the Giants. She is a tall, slender woman who wears white fur and a gold crown, and carries a wand that she uses to turn creatures into stone and conjure enchanted food. The White Witch represents greed, as well as the power of evil.

It is important to note that the White Witch was previously the Emperor's hangman, and that it is her right, in accordance to with the deep magic stemming from the dawn of time, to kill traitors.