In a persuasive essay, your job is to persuade somebody to join to do something new and exciting, in a philosophical way.
In a expository essay, your job is to inform, explain, describe, or define how well you know a certain topic. Keys to this essay is deep info, and staying on track on the topic.
In a Narrative essay, your job is to recreate or create a story that you know or that you make up and write about what happens in an engaging way.