If you make a prediction and it comes true, your words were prophetic. Like the time you warned your dad against eating a whole box of donuts. He got sick, right? That was a prophetic warning.
The adjective prophetic traces all the way back to the Greek word prophētikos, meaning "predicting." You know who's really good at predicting stuff? Prophets. Usually, prophetic is used to describe a thing — like a warning, a feeling, or a complaint — rather than a person.