This exercise introduces two concepts: the roles of a hero, and dynamic characterization. Both are pretty simple to grasp; however, too often, authors only concentrate on one or the other but not both of these things simultaneously, and it ends up hurting the story.
First, let's define the concepts.
A hero has several roles in a story. His (or her) relationships, relatives, occupation, etc. help define them in terms of the plot, but the hero also plays an important part in keeping the reader's interest... and so, another role of a hero is to relate to the reader, thus in turn allowing the reader to relate back. Finally, a hero's motivation is usually a role, too. It might seem odd to think of it this way, but if Bob's motivation is, "I want a doughnut," then at least at the moment, his role in the story is to be the person trying to get a doughnut. (By similar logic, any person who is motivated to stop Bob from getting a doughnut will play the role of antagonist--assuming Bob is the protagonist in this tale.)
Dynamic characterization is merely the principle that any character's roles (doesn't have to be the hero's) should change over the course of the story. A character who does not shift roles is static. But this is not all we mean by "dynamic characterization." The principle also states that the inward traits of the character should change over the course of the story.
The key to understanding dynamic heroes is that the shifts of their inner traits and their shift in roles go hand in hand, and furthermore, one is usually the cause of the other. Note that it can go both ways.
Your assignment: Consider, for a moment, the character Julie Smith.
Julie grew up in Milwaukee and was never rich. Her father died when she was thirteen, and her mother could not pay the bills on her own... So Julie worked to help her mother support the household (Julie has two younger brothers). Later, Julie became the first in her family to graduate from college. She wants to become a doctor and go to medical school... But her mother wants her to get a job and/or a husband, instead.
Write an entry in Julie's diary on the day she sends in her medical school applications against her mother's wishes. Hint: a good writer will do more than just recall the background; realize that this is another step along the road for Julie, and that her life will be different after this day because of her decision--whereas in the past, perhaps, her life-changing events had mostly been beyond her control. Show us what thoughts Julie has during this transition in her life. What is she afraid of (besides the obvious, confronting her mother)? What is her motivation? Why?