If your teacher gives an explanation of a difficult text you are reading, she is giving you an exegesis on it. An exegesis is a critical look at a text.
Exegesis comes from the Greek word for interpret and it's often used in connection with the Bible. Often times, religious rules are based on an exegesis of a text. For instance, some Jewish people do not eat meat and dairy in the same meal based on an exegesis of a law in the Torah that says you should not eat a calf cooked in its mother's milk.