The Enterprise crew looking at supernatural spirits
The supernatural referred to anything that appeared to transcend the laws of nature.
This could include things such as black magic, ghosts, goblins, demons, zombies, vampires, fairies, and anything rooted in mysticism and superstition.
In 2268, when the Enterprise traveled to Kalandan outpost, Captain James T. Kirk referred to it as a ghost planet, due to the unusual phenomenon associated with it, as it was too young of a world to have life on it. Spock, however, disagreed, saying he didn't see anything supernatural about the planet, despite his inability to give a scientific explanation. (TOS: "That Which Survives")
In 2269, when Lucien transported Kirk, Spock, and McCoy to Megas-Tu, they initially found themselves to be of a strange ghost-like form, which was unsettling to them, and because of this, Lucien used his magic to make them appear in a form more to their liking, as they would look in their own universe, but he told them holding them together like that wasn't even natural. (TAS: "The Magicks of Megas-Tu")
In 2366, the Mintakans viewed Jean-Luc Picard as a supernatural being. (TNG: "Who Watches the Watchers")