I believe that any perceptive teacher can see what his students really need emotionally in order to succeed far beyond mastery of the basic lessons he imparts daily. When a teacher is able to relate to a student on a deep level, teaching turns into mentoring.
To me, a teacher is a person whose priority is to educate their students on specific content. In contrast, a mentor is a person who not only lectures on specific subjects, but also has an underlying leadership philosophy that positively influences others as they move through life. He will inspire them to pursue their dreams and fulfill their true potential beyond the basics.
In order to become a mentor, first you need to become aware of the role you have in the eyes of your students and become intentional in the way you are interacting with them. If you are successful, you will find that the students are mentoring you just as much as you are mentoring them. Thus, if you are going about it correctly by working with them as individuals, the benefits will be priceless.