The idea that you can see the future by supernatural means is called divination. When your friend tells your fortune by reading the tea leaves in your cup, she claims to have the power of divination.
The prediction or prophecy itself that's given through the act of fortune telling is also called divination. A psychic's divination that your aunt will soon start a family is much less impressive if your aunt is obviously pregnant. You can also use divination to refer to someone's unusual intuition, like a child who seems to know by divination when someone is feeling sad or upset.