Writing in an expository style means that you are providing the reader with information. You also need to explain and describe that information. Your essay will probably need to consist of five paragraphs—an introduction, three body paragraphs, and a conclusion.
So, when it comes to an expository essay about what family means to you, I would use the introduction to introduce the members of your family. In a stereotypical nuclear family example, this would be your parents, siblings, and perhaps some cousins.
Use the three body paragraphs to discuss what family means to you, using examples of stories involving the people you introduced in your introduction.
The conclusion needs wrap up your essay in such a way as to provide a definite answer to the question that was posed.