During the Angel Invasion Paul killed one of the Angels with the Sword of the Fallen.
This angel was called Noriel.
After Noriel reincarnated as a mortal, a demon found it and performed a ritual on his human girlfriend, Linda Danvers, to transfer all of the angels knowledge into her, but he also accidentally copied Noriels personality and it was fighting for control of the body, but he apparently did something to help Linda out, however OL later on disrupted whatever that was and now Noriel and Linda are either merged, or Noriel is the dominant personality, because an ancient angel versus an emotionally immature and unstable teenager tends to go in the favor of the angel.
After that said beings called itself Loriel.
Loriel primarily uses fire and may have other powerful magics at her disposal.
She also calls herself Supergirl, because Linda tried to frame Kara, who in this story still hasn't taken on the title of Supergirl and may not become a superhero, and now just calls herself that.
This is a re-imagining of the comic Linda Danvers version of Supergirl.
That version basically had some plasma entity from another universe bond to her and later on started calling herself Supergirl, while in this story she was bonded to an angel.