Supernatural (and/or paranormal) typically refers to phenomena which are not bound to natural laws or observability. Because of this, science cannot and does not attempt to explain these phenomena, as they are untestable and cannot be substantiated with empirical evidence. When asked for evidence to substantiate their claims, believers in supernatural phenomena usually offer hearsay or personal anecdotes.
Throughout human history, there have been many claims of supernatural events or supernatural abilities. None of these claims have ever been demonstrated to be true. Furthermore, many of these claims are mutually contradictory, and people who believe in one form of paranormal activity will usually not believe in others. Thus, a devoutly religious person may regard ESP or witchcraft as nonsense. It can be very useful to apply the outsider test when debating against a specific supernatural claim: if your opponent can understand why they don't believe competing supernatural claims with similar evidence, they can better question their own beliefs.
In other cases, claims are simply not falsifiable, and testing them has no purpose. For example, prayer. If one prays for X, and X happens, they can attribute this to whatever figure they prayed to. However, if X does not happen, it is often rationalized by stating "it wasn't ready to happen yet" or "this means I'm focused incorrectly, and don't need it." With these rationalizations, prayer is not falsifiable, and becomes indistinguishable from coincidence or chance. Often times, one can replace the figure they prayed to with any other thing (for example, a brick or carton of milk ), and the "argument" for prayer now "demonstrates" a completely different thing.