Supernatural (and/or paranormal) typically refers to claims of phenomena which science cannot explain.
In the entirety of human history, not one claimed occurence of a supernatural event nor one claim of supernatural ability has ever been reliably proven. In fact, not one shred of verifiable evidence has ever been provided for any supernatural claim.
Often, people who believe in one form of paranormal activity will not believe in others. Thus a devoutly religious person may regard ESP or witchcraft as nonsense. This is a very useful fact to keep in mind when debating the issue.