Check out my post on this topic over at the Women in Astronomy Blog. An excerpt:
Mentoring is distinct from teaching and academic advising, but not necessarily separate. An academic adviser or teacher can serve as a mentor, but in my mind the processes of advising and teaching are separate from the process of mentoring. Mentoring is based on a personal relationship, often with someone with a set of shared experiences. The mentor's role is to serve as a guide for the mentee, to help them develop professionally and personally.