Powers: Telekenesis and telepathic. That means that she can lift things with her mind and can read your mind. (Never lie to this women when she is holding up your car and you're under it!)
Past: You do not learn about her past from the movie.
Introduction into movie: She is shown trying to give Logan an injection. (The keyword is try!)
Importance to the movie: She helps a little during the climax, but that's about it. She also gives a little insight to Logan's past.