1.
former teacher, mentor, teacher to whom one is indebted
A teacher or mentor who had a significant positive influence on one's life. The word carries deep gratitude and respect, going beyond just 'former teacher' to imply a lasting debt of gratitude.
Usage
A respectful word that expresses gratitude. You would not normally use 恩師 to refer to a teacher you disliked or who had no particular impact on you. The word implies a significant personal debt of gratitude (恩, indebtedness).
Cultural note
In Japan, the student-teacher relationship is often maintained long after graduation. Visiting one's 恩師 or keeping in touch is considered an expression of proper gratitude.