noun
an inner or attendant spirit or inspiring force Socrates claimed to have lived his life according to the dictates of his daimon
noun
In short, they are your soul. The spelling is taken from the His Dark Materials books. The concept in the books was taken from Aristotle's concept of a daimon who was his spiritual guide.
A daemon in our world is incorporeal, more of a voice in your head. When people visualize them, they are usually animals. They can shapeshift to almost anything. Eventually they will settle as an animal that reflects your personality and character the best.
My daemon is settled as a red fox.