These sorts of essays seek to give the reader information about a topic. Usually, an expository essay seeks to persuade the reader to think, act, or believe something. The characteristics of an Expository Paper are a clear thesis, 3 or more reasons for supporting the thesis, examples which explain those reasons and a conclusion which tells the reader what they need to think about the thesis.
"Expository" is a broad term and often writing classes will divide expository writing into a variety of categories. Here are some examples:
Describing: painting a vivid picture of a time, place or experience.
Persuasive or argumentative: giving reasons for the reader to believe your idea.
Comparison: telling how things are alike and different.
Narrative, personal experience or reflection essay: telling a story that has a meaning.
Explain: instructing by telling process or how to do something.