An expository essay is an essay that makes a point by explaining why something is as it is. If you're writing an expository essay about yourself, the first step is to decide the most important point you want to make and explain about yourself. I assume everyone in class is doing the same assignment, so you don't have to worry too much about appearing overly vain.
Your topical choices are numerous. Generally you'll want to choose three things, so start looking at categories of things which would give your readers both an accurate and interesting picture of who you are. Some ideas include writing about your likes/dislikes; hobbies/interests; family; talents/skills; changes; jobs...and the list goes on indefinitely.
As part of your explanation, you might be to take three things which are meaningful to you but also reveal something interesting about you. Perhaps you'd choose your car, your backpack/book bag, and your jewelry box. If you've lived in three houses, that might be an effective way to talk about three periods or eras in your life. You might also choose three quotes which exemplify you or three things you passionately believe and how they've shaped who you are. Maybe you have three influential people who have helped shape you into the person you are today. Once again, your choices are unlimited.
Whatever you choose, make sure it's a reflection of the point you want to make about yourself. You can be as self-revelatory as you want to be. Your fear of appearing too vain is valid, but you can't let it paralyze you. Be sure to give credit to others in your life who have helped you and to avoid excessive use of personal pronouns (I, me, my, myself, mine). This is an interesting assignment, and I'd encourage you to find an interesting personal angle from which to write. Best of luck!