Another way it could be used is to represent a character's journey of self - discovery. For instance, Caroline, as she evolves from a self - centered teen to a more empathetic and powerful vampire. The song's idea of running up a hill can symbolize the challenges she faces in growing and changing, and the idea of making a deal with God (or in the context of the show, perhaps a higher power like the witch spirits) to ease that journey.
The song could be used to set the mood in a particular scene. If a fanfic writer is creating a tense moment, perhaps when the vampires are facing a new and powerful enemy, 'Running Up That Hill' might play in the background of the story. It could add an element of drama and mystery, as the characters strive to overcome the odds against them, much like the uphill battle described in the song.