What you are reading right now is an example of a paragraph, and in replying to your question, I will be using several paragraphs to help explain how and we use paragraphs.
Paragraphs are used in formal writing to make text easier to read. If you were reading a newspaper, magazine or novel, the text would be difficult to take in if the author presented his writing in one continuous block of words. So, dividing up the text into blocks of differing lengths makes both reading and absorbing information easier.
A good paragraph will contain one central idea or theme, and the next paragraph develops that idea further, or present a new idea. If you are reading a novel, a new paragraph may indicate a change of setting, the passage of time, or a different character or set of characters than feature in the previous paragraph.
How to Use Paragraphs in Your Own Writing
Paragraphs give your writing structure, and helps the reader to identify and follow the development of your ideas. Remember, paragraphs should have their own internal structure and fit into the larger structure of the piece.
Be clear what the main idea for each paragraph is, deal with it fully, while avoiding digressions and irrelevancies. Good use of paragraphs is achieved when the reader can get a reasonable grasp of the content of your writing by reading the first sentence of each paragraph.