This is a really broad question, but here are a few things for you to think about in regards to Jay Gatsby.
1. He lives on West Egg, the "new money" side of town.
2. He throws lavish parties in the hopes of attracting Daisy's attention.
3. He is likely involved in gangster activities as evidenced by his assocation with a man like Wolfsheim.
4. He has loved and longed for Daisy for years, and has accumulated great wealth in an effort to regain her.
5. He has actually had grand ambitions since childhood, so Daisy isn't his only motive.
6. He has a naive and optimistic view of life -- he even thinks you can repeat the past.
7. He is loyal to Daisy, even when it becomes apparant to us that he will never truly get her back.
All of these elements of his characterization play into the most salient of the themes of the novel: the achievement and decay of the American Dream; true love; reality vs. illusion; the moral corruption of society, especially of the upper classes; infidelity; honesty/dishonesty; and the list could go on.
In order to respond to this task, you need to consider some specific thing you know about Gatsby, and then connect it to some specific point that Fitzgerald is making throughout the novel. You can take the above lists and start making some connections there, and then you can fill in with other details of Gatsby's character and connect those to a specific theme or themes.