What is the purpose of mystical creatures in a story?
Often they represent and exploit the vices in a person or humanity, the repressed or unconscious desires, fears of people. They can also be a "doppleganger" of a character showing a different side of a character. Of course, they add excitement and interest with their seeming impossible existence. It does depend on each individual story and creature that are mentioned though and on the interpretation of the reader.
I think they are there so we can escape reality for a while, even though we might have in our behavior, i think the fact that they dont look like us and some even have supernatural power, it entertains us and it makes some daydream and all that, makes us desire that different world with rare creatures and just plain different from the World we live in. I think theyre just an attraction
What qualities or attributes make them interesting?
To make it more interesting.