Yuzuruha, like Kongiku, is a fox spirit, or Kitsune that is a servant to Inari. She is able to assume human form and is hardly ever seen in her original fox form.
Yuzuruha meets Kisuke shortly after he lost his memory. Seeing his potential as a sword fighter she gives him the mask that contains Muramasa, allowing Kisuke to craft the demon blades, as long as he in turn supports Inari by delivering souls of his enemies. She then guides him throughout the story, including telling him info about different places, and informing him about the main Inugami antagonist in Kisuke's story. She can be found at any of Inarigumi's shrines, which act as save points. She can also sometimes be found and spoken to in Hot Springs, and will tease Kisuke or offer to perform tasks such as washing his back.
At one point Kisuke asks her to act as a cupid for him and Torahime and indeed Yuzuruha takes this role after both Kisuke and Torahime have been reborn and consequently lost their memories.