For example, an unexplained healing is regarded as a miracle. So would be resurrection from the dead. But miracles are generally regarded as tangential to one's faith life.
Why? Well, one reason is because it is pretty easy for someone who adheres axiomatically to materialist philosophy to rationalize any miracle or supernatural with a natural explanation. For example, an atheist might believe that it is impossible to levitate, so would explain any report of a levitation as a lie or misunderstanding.
But what if an atheist witnessed a levitation? Even then, the atheist could believe that he halucinated. Or sometime later come to believe that his memory was faulty. So even first-hand observation might not suffice.
That's why I like to point to the Shroud of Turin as an example of the supernatural to hardened skeptics. Here we have a natural phenomenon, an image on a cloth, but lacking a natural explanation. Moreover, the phenomenon is persistent, it has existed for years, and has been subjected to endless, rigorous scientific investigation. It's impossible to explain in materialist terms. Which explains why many atheistic or agnostic scientists who have examined the cloth have converted.