What does it mean to capture the history around the characters in relation to Water for Elephants?
This is rather a broad question. One way of answering it would be to say that it is important, as part of understanding a character as fully as we can, to think about and consider the history of that character and what has happened to them in order to full appreciate where they are in the time of the novel and what factors have been responsible for making them the kind of people that they are today. One example would be to consider the character of Marlena and how we are told she met and married her violent husband, August. This enables us to gain a fuller understanding of her character and helps us to know why it is that she made the decision to marry August in the first place, when he seems to have so little to recommend him.
You also might like to consider how capturing the history helps us to understand Jacob better. The initial chapters that inform us about the loss of his parents and how he loses all his belongings in the world because of their generosity helps us to understand why he chooses to leave everything and escape, getting onto the next train without knowing where it will take him and being able to enter a radically new world from anything he has ever experienced before. Background and history is crucial for gaining a full picture of character.
The personal histories of the characters in a story are essential to an understanding of their character arcs -- how the characters change during the story. This is particularly important for the protagonist, who is essentially the one the story is about and the character with whom most readers / viewers relate. In Water for Elephants, Jacob is the character we tend to care about most. His history works to define him. A veterinarian, save the final certification, Jacob's compassion for the elephant and the horses determines his role in the traveling circus. His compassion extends to his concern for Marlena. He is hungry and impoverished (as so many others were at the time), but he eventually finds his backbone.
That said, character action must be seen to play against that backstory that is revealed to us over the course of the film / book, and character action must be placed in time -- in the historical landscape that can strongly influence character action. Extreme economic conditions tend to enlarge character attributes. Traits such as honor, compassion, selflessness, selfishness are all exaggerated by adverse conditions. Jacob's nature looms in high contrast to the dog-eat-dog environment in which he finds himself. Marlena compromises her integrity and pride in an effort to keep live on an even keel -- as much as possible, that is, given August's mood changes and violent streak. The less worldly Jacob at first reels in this tide of desperation and deceit, until he finds his footing and his courage gains traction.
Consider how differently Jacob's story would have played out if he were not from a loving home and a relatively privileged background. It is the placement of Jacob in chaotic times, where people must rely on their wits to survive -- where compromise has lost its meaning -- that creates the tension. If Jacob had been a street-wise shark -- if the times had not been extraordinarily difficult --Water for Elephants would be a different story altogether. Character history and historical placement come together in this story in a powerful way.