Exposition is a type of oral or written discourse that is used to explain, describe, give information or inform. The creator of an expository text can not assume that the reader or listener has prior knowledge or prior understanding of the topic that is being discussed. One important point to keep in mind for the author is to try to use words that clearly show what they are talking about rather then blatantly telling the reader what is being discussed. Since clarity requires strong organization, one of the most important mechanisms that can be used to improve our skills in exposition is to provide directions to improve the organization of the text.
You can follow the link for expository organizational patterns

An essay is an extended piece of writing that presents and supports a thesis or proposition. The word ‘essay’ derives from the Latin word ‘exagium’, meaning the presentation of a case.

When you write an essay you are making a case for the validity of a particular point of view, analysis, interpretation, or set of facts or procedures.

Keep in mind directive verbs .
Directive verbs are those that give instructions about what you are required to do in the essay. Make sure you understand these words. Below is a list of the more common directive verbs used in essay briefs.

Example of Directive Verbs

Analyse
Break something down to identify the main ideas and component parts then show how they are related and why they are important. |
Interpret
Give the meaning.  You give your own opinions, backed by evidence.
Comment on
Discuss, criticise or explain the meaning of a situation or statement. |
Justify
Show why you think it is right.  Give reasons for your statement or conclusion.
Compare
Show both the similarities and the differences. |
Outline
Give a general summary of the main ideas, supported by secondary ideas.  Omit minor details.
Contrast
Compare by showing the differences. |
Prove
Show by argument or logic that it is true.  You must provide adequate evidence.
Define
Give the exact meaning. |
Relate
Show connections.
Discuss 
Examine, giving the details and the points for and against.  You must develop a logical argument backed by sound evidence. |
 Review
Make a survey in which you look critically at the important parts.
Enumerate   
List, name, and specify and describe the main ideas. |
State   
Specify the main points in precise terms.  Omit minor details.
Evaluate 
Give your judgement, after showing the advantages and disadvantages. | Summarise     
Give a concise account of the main ideas.  Omit details and examples.
Explain
Make plain, interpret, and account for in detail. |
Trace
Follow the progress or history of a topic.
Illustrate
Explain or make it clear by concrete examples.  Sometimes you may use a figure or a diagram. | 

Analyse
Break something down to identify the main ideas and component parts then show how they are related and why they are important. |
Interpret
Give the meaning.  You give your own opinions, backed by evidence.
Comment on
Discuss, criticise or explain the meaning of a situation or statement. |
Justify
Show why you think it is right.  Give reasons for your statement or conclusion.
Compare
Show both the similarities and the differences. |
Outline
Give a general summary of the main ideas, supported by secondary ideas.  Omit minor details.
Contrast
Compare by showing the differences. |
Prove
Show by argument or logic that it is true.  You must provide adequate evidence.
Define
Give the exact meaning. |
Relate
Show connections.
Discuss 
Examine, giving the details and the points for and against.  You must develop a logical argument backed by sound evidence. |
Review
Make a survey in which you look critically at the important parts.
Enumerate   
List, name, and specify and describe the main ideas. |
State   
Specify the main points in precise terms.  Omit minor details.
Evaluate 
Give your judgement, after showing the advantages and disadvantages. | Summarise     
Give a concise account of the main ideas.  Omit details and examples.
Explain
Make plain, interpret, and account for in detail. |
 Trace
Follow the progress or history of a topic.
Illustrate
Explain or make it clear by concrete examples.  Sometimes you may use a figure or a diagram.

Exposition is explanatory communication, whether in speech or writing. So an expository essay is an organized piece of prose which explains a specific topic or set of ideas to a defined audience.

Expository essays provide information and analysis. An expository essay may or may not have an overt central argument, though it does set forth points of view on the topic. It differs from the persuasive research paper in the level of research and argument it employs. While an expository essay should be focused on a particular topic and illustrate its points with specific examples, it doesn’t usually have the depth of research or argument that you need in a major research assignment. With an exam or a standardized test, for instance, the examples you use to support your points will be based on the knowledge already inside your head.

An expository essay does have certain baseline requirements that are standard in nearly every essay type:

How Do You Write an Expository Essay?

One common formula for the expository essay is the 5-Paragraph Essay. If you don’t have much experience with essay writing, this is a good method to start with, since it’s basic and straightforward. The 5-Paragraph Essay incorporates the elements listed above in the following basic structure:

While the 5-paragraph structure gives you a helpful formula to work with, it’s only one among many valid options, and its suitability will depend on other factors like the length and complexity of your essay. If you’re writing a paper that’s more than 3 or 4 pages long, it should be more than 5 paragraphs. In most cases, the structure of a longer essay will be similar to that of the 5-paragraph essay, with an introduction, a conclusion and body paragraphs performing the same basic functions—only the number of body paragraphs will increase. The length of the paragraphs may also increase slightly in proportion to the length of the essay.