A paragraph is a complete thought. This follows from one of the definitions of a sentence: a single thought. A complete thought usually consists of a group of sentences all of which are related to a central thought, topic or idea. If part of a topic or idea is to be emphasized, it should be placed in a separate paragraph.
The purpose of a paragraph is to make communication with the reader easily understood. A paragraph keeps segments of the composition unified by helping to prevent digressions from the central idea. A new paragraph gives the reader a breathing and thinking break because the reader knows one topic is concluded and another is to begin.
Conversational statements, replies and exclamations can be one-word paragraphs, but in narrative, descriptive or expository writing, a paragraph is a minicomposition, most often written in the order of occurence or observation. Some magazine articles use long, well-developed paragraphs, complete with one or two topic sentences, a detailed development of the topic and a summary statement or two.
Here is an example using a business letter. Sentence 1 is the topic; it refers to disposal of equipment. Middle sentences provide details about the disposal. Sentence 4 summarizes the subject by suggesting action to be taken.
(1) I agree with your letter of March 25, 19—, except for the part
referring to disposal of leased equipment. (2) The lease says that so long
as the value of the plant is not materially affected, the lessee may dispose