A paragraph is a basic unit of organization in writing in which a group of related sentences develops one main idea. A paragraph can be as short as one sentence or as long as ten sentences. The number of sentences is unimportant; however, the paragraph should be long enough to develop the main idea clearly.

A paragraph may stand by itself. In academic writing, a paragraph is often used to answer a test question such as the following: "Define management by objectives, and give one example of it from the reading you have done for this class."

A paragraph may also be one part of a longer piece of writing such as a chapter of a book or an essay. 

A paragraph has three major structural parts: a topic sentence, supporting
sentences, and a concluding sentence.
The topic sentence states the main idea of the paragraph. It not only names the topic of the paragraph, but it also limits the topic to one or two areas that can be discussed completely in the space of a single paragraph. The specific area is called the controlling idea.

In addition to the three structural parts of a paragraph, a good paragraph also has the elements of unity and coherence.
Unity means that you discuss only one main idea in a paragraph. The main idea is stated in the topic sentence, and then each and every supporting sentence develops that idea. If, for example, you announce in your topic sentence that you are going to discuss
two important characteristics of gold, discuss only those. Do not discuss any other ideas,
such as the price of gold or gold mining.
Coherence means that your paragraph is easy to read and understand because your supporting sentences are in some kind of logical order and your ideas are connected by the use of appropriate transition signals. For example, in the paragraph about gold, there are two supporting ideas: Gold is beautiful, and gold is useful. Each of these supporting ideas is discussed, one after the other, and an example is given for each
one. This is one kind of logical order. Furthermore, the relationship between the ideas is clearly shown by using appropriate transition words and phrases such as first of all, for example, another important characteristic, and in conclusion.
In summary, a well-written paragraph contains five elements: a topic sentence, supporting sentences, a concluding sentence, unity, and coherence.

POSITION OF TOPIC SENTENCES

The topic sentence may be the first or last sentence in a paragraph. The topic
sentence may also be the first and last sentence of the paragraph - "sandwich-style." A sandwich-style paragraph is especially helpful to your reader if the paragraph is very long. The second topic sentence in the sandwich-style paragraph also serves as a concluding sentence.

RELATION BETWEEN TOPIC SENTENCE AND SUPPORTING SENTENCES
Good supporting sentences are related to the topic sentence and its controlling
ideas. Supporting sentences are like the foundation of a house. If a house does not have a good foundation, it will collapse. Likewise, if a paragraph does not have good supporting sentences, its meaning will collapse, and readers will not be able to follow the ideas. The paragraph may be confusing or illogical.
Good supporting sentences give information that supports and explains the topic of the paragraph. They answer questions - Who? What? Where? When? Why? and How? – and give details. Good writers think of these questions when they write support—that is, supporting sentences - for the topic sentence.

A concluding sentence is not absolutely necessary; In fact, a concluding sentence is not customary for every paragraph in a multi-paragraph essay. However, for single paragraphs, especially long ones a concluding sentence is helpful to the reader because it signals the end of the paragraph and because it is a reminder of the important points.

A concluding sentence is not absolutely necessary; In fact, a concluding sentence is not customary for every paragraph in a multi-paragraph essay. However, for single paragraphs, especially long ones a concluding sentence is helpful to the reader because it signals the end of the paragraph and because it is a reminder of the important points.