Abilities: Creation of any kind of medicine; natural genius
She's a person from the moon. That means she's an alien. She has lived on the Earth for a long time. Her relationship with Kaguya dates back to their days on the moon.
The Yagokoro family is a line of medicinal geniuses that have been living on the moon for some time. Even among them, Eirin is exceptionally intelligent. She is much smarter than humans, which makes her rarely understood.
In truth, she has power well beyond that of Kaguya's. She saves her power and maintains it at a lower level out of respect for Kaguya.
Long ago, Eirin was one of a party of messengers who were sent to bring Kaguya back to the moon; the crime for which she was exiled to Earth had been forgiven. For some reason, she helped Kaguya kill all the other messengers instead. To ensure that the earthlings who lived with Kaguya would remain silent, she bribed them with the Hourai Elixir. The elixir had the power to make people immortal. None of those earthlings consumed the elixir, however, and died shortly afterwards.