Generally, class essay assignments ask you to discuss in some depth a topic relevant to the course content. While analysis is the basis of most essays, other goals can be included, such as speculation, evaluation, etc.
Essays require the ability to establish and maintain a focus on a topic.
Typically, an essay is organized by introducing your topic, explaining and supporting the focus, and then drawing some relevant conclusions from your discussion and analysis. As a rule, do not simply rely on generalizations to express your ideas. Also, because an essay tends to involve abstract concepts, it is always a good idea to make sure that those concepts are defined, so that both you and the reader share an impression of what you mean by an idea. The essay format can often provide the basis for other types of writing. Many other types of writing are based on analysis, as an essay generally is, and many also often rely on its overall organizational scheme.