Never heard of Inuyasha before

No, this is the second movie based on a TV series called Inuyasha. The premise is that Kagome is the reincarnation of the priestess Kikyo. On her 15th birthday, she falls through a well at her family's shrine and is transported back in time to feudal Japan, only in this feudal Japan demons and magic abound. Kagome comes across a boy transfixed to a tree, only this boy has dog ears! This boy is Inuyasha, a half human, half dog-demon. Together, they have to seek the pieces of the Shikon no Tama, or Jewel of Four Souls, which Kagome accidentally shattered. I could go into more detail, but I haven't seen the movie yet, so I don't know how much you would know already. It's a great series, so I highly recommend watching it!

Part of the story is a bit based on Taketori Monogatori - The Bamboo-Cutter's Tale - something that Kagome mentions while sitting at the fire. Tketori Monogatari starts with a childless elderly couple, the husband being a bamboo-cutter. One day, he finds a stalk of bamboo glowing as he is out cutting bamboo, and when he cuts it down, there is a tiny girl-child inside. He brings her home, and he and his wife raise her, naming her Kaguya. Subsequently, more glowing bamboo is found, with piles of gold coins inside. This allows Kaguya and her family to move to the city, never wanting for material possessions. Kaguya (called Kaguya-hime, or Princess Kaguya) has grown up in a remarkably short amount of time, and begins to attract suitors because of her beauty. All but five she discourages to the point of giving up on her hand. These last five, she charges each with an impossible task, some item to find for her. The Jewel of the Dragon's Throat, the Jeweled Branch of Hourai, the Cloak of the Fire-Rat, the Swallow's Cowrie Shell, and the Stone Cup of Buddah. One disappears during his quest, others try to fake their items, but Kaguya easily figures them out and sends them away. Then, she announces that she is the princess of the moon, sent to earth during a great war on the moon, and now she has to return to her kingdom at the next full moon. The bamboo-cutter and his wife protest, and guards are hired to keep her from leaving. However, on the night of the full moon, the guards all are put to sleep, and the bamboo-cutter and his wife watch tearfully as Kaguya is guided away by an unearthly procession of maidservants and courtiers.

Well, the movie's main characters are from the InuYasha series, but Princess Kaguya is from Japanese mythology. Kaguya's story is about an elderly couple and the old man cuts bamboo for a living. One day, he cut a shiny bamboo stalk and found a baby inside. He named her Princess Kaguya (Kaguya=shining light). Years later, she told her parents that she was of the moon and she would have to go back. Not wanting her to go away, the old man sent guards to protect her. But moon people came and took Kaguya away anyways. I thought it was kinda cool to see something from the ancient stories that I love in another story I adore.