What is the purpose of an expository essay?
To expound on a selected topic.
An expository essay explains a topic, put simply. It can be a "how-to" essay or an essay on the history of Chinese emperors. When you write these essays, write them in the third person. There should not be an "I," "you," "me," etc. anywhere. Remember, you're stating facts, so this is a very non-personal type of essay. Just say "this happened." Don't say "I think this happened." Do that, and you'll be fine!