Without knowing the specific book that your question references, I am going to have to pick a book of my own and answer the rest of the writing prompt.  The general gist of what you are being asked to do is illustrate how character actions help an author develop an intended theme.  

In order to start this kind of literature analysis, you should start by coming up with a thesis statement.  For my book, I will choose The Chrysalids and my character will be David Strom.  A thesis that relates a theme to a character from this book could be something along the lines of "David Strom helps convey the theme of anti-discrimination."  

Following a thesis that you are happy with, your next job is to find evidence from whatever text that your thesis is based on.  A solid thesis is important, but you absolutely must back it up with specific examples from the text.  One reason why David might be so willing to accept genetic differences within Waknuk society is because he is genetically a deviant himself.  Of course he does show signs of acceptance before he even knows of his mutation.  For example, he doesn't turn in Sophie after discovering she has an extra toe. I would pick three to four strong examples from the text and then write a conclusion.  

To approach this essay prompt, you might pick a work of literature and either think first about the themes of the work or think about the major characters in that work.

If you start with the themes you will then pose the question, "How do the major characters express or relate to this theme?" If you start with the characters, you will ask, "What is the meaning behind this character's story and decisions?"

The goal here is to see how a character's decisions (and so that characters (1) conflicts and (2) actions) relate to a literary work's meaning, commentary, or artistic statement. 

Let's take Shakespeare's Romeo and Juliet as an example. One of the play's major themes is impersonal social conflict - or, more specifically, how entrenched impersonal social conflict has very personal repercussions yet individuals are largely powerless to overthrow the existing social order.  

After identifying this theme, we can examine the text for material that expresses this idea or that articulates the idea via dialogue or action. Looking for evidence of this theme in the text, one quickly sees that the characters of Romeo and Juliet repeatedly give voice to the idea of intractable social conflict.

Juliet says, "My only love sprung from my only hate!" 

And from the play's opening lines, these characters are set up as examples of how a long-standing familial conflict will not be lightly or easily overcome.

Two households, both alike in dignity,
In fair Verona, where we lay our scene,
From ancient grudge break to new mutiny,
Where civil blood makes civil hands unclean.

Thus Romeo and Juliet are characters that function in the text as an expression of the play's central theme of impersonal social conflict. Other characters also serve to forward this theme in the text, but no one more fully than the two protagonists. 

Writing an essay on this subject, your thesis will state that the characters of Romeo and Juliet are used in the text as expressions of Shakespeare's theme in the text relating to the entrenched nature of social conflict.

Since you did not specify a particular novel or character, let me address this generally.   I would use this part of the prompt to craft my thesis:

"Using characters form the following books, analyze how the dangers or choices these characters have to make are used by the authors to develop their themes."

Simply reword the prompt to convey your argument.  Here is an example using Lord of the Flies:  In Lord of the Flies, William Golding utilizes Ralph's struggle against Jack's egotism to develop his theme of civilization versus savagery.   Then you should search for examples from the text to support your claim about that character.  Look for strong moments or challenges that the character endures or overcomes that speaks to the main theme of the novel.