Paragraphs are the building blocks of any piece of writing, but take different forms depending on the genre of the text. For example, in journalism, paragraphs tend to be very short, sometimes only a single sentence, whereas in a literary text, paragraphs may take any form depending on the author's style. Academic writing has its own paragraphing conventions.
The function of the academic paragraph is to make a single point in the argument, to set out one of the links in the chain of reasoning. It is a self-contained point, which together with the other paragraphs contributes to building the argument. The order of the paragraphs constitutes the structure, but is also one of the places you can articulate that structure.
The paragraph makes the point and also develops it. This development might be examples, explanation, evidence, exploring variations in interpretation, analysis, etc, depending on the point to be made (it is not just explaining or 'backing up' the point, although this is part of it). It is not possible to state how long a paragraph should be, but a paragraph that is too short does not develop the point enough, and a paragraph that is too long is probably confusing and conflating more than one point.
Presentation and layout can also impact on the way your reader perceives your structure. English essays often contain many long quotations from primary texts, especially verse or drama, which must be presented separately from the main text of the paragraph, as described in the Faculty's guidance on portfolios of essays:
Quotations of a sentence or less, or verse quotations of two or three lines only, should be incorporated in the body of the essay, enclosed within quotation marks; the line-endings of verse should be indicated by a diagonal stroke (/). Quotations exceeding these lengths should be separated from the body of the essay by a double space, and set as a separate, single-spaced block, not enclosed in quotation marks.
Take care through use of line spacing and indentation that this presentation is not mistaken for a paragraph break; this can confuse the reader as to where your paragraphs begin and end, meaning that they lose sight of the points you are making and your structure. The house style in the Faculty of English is to indent the start of each paragraph.