Having an existence outside of the natural world. In this sense, everything supernatural is also preternatural.
beyond, Beyond or different from what is natural or according to the regular course of things; therefore something which is strange; inexplicable; extraordinary; uncommon; irregular; or abnormal. This more limited sense is often used to describe things which are fully in the natural world, but are merely extreme examples.
Her hearing allowed her to hear the cricket chirping, when the rest of us couldn't hear anything. (rfex)