Aoko Aozaki is a lady that Shiki met in his childhood years. At the time, Shiki was still under hospital care and recovering from his accident which caused him to see lines that no one else could, and Shiki suddenly got special powers that he didn't know how to use properly.
It was she who gave him a special pair of glasses that block the lines from his vision. However, the biggest gift that she gave him was the meaning and will to live his life in a good way. She taught him to never use his Mystic Eyes with the intention of killing, but instead to use them to protect those he cares dearly about.
She doesn't like her name (since it sounds like Blue Blue - Ao = Blue), so Shiki decides to call her "Teacher". (Note that Shiki never referred to anyone else in his life as teacher; that's how much he respects her.) She seems like a nice person but she actually has a rough personality.
She is a mage from the Mage's Association. Although, she isn't just an ordinary mage, but one of the five great magic users still alive. People know her as "Magic Gunner, Miss Blue" and fear her power. Although her actual magic is a mystery.
She also has a sister that appears in the parallel story of Tsukihime, Kara no Kyokai. The glasses that she gave to Shiki were actually stolen from her sister, Touko.
(Source: The Moonlit World, Absolute Anime)
