Theory:

A group of sentences formed together related to one particular topic, or develops to a single point, is called a paragraph.
A paragraph in simple words is a group of sentences. Take any book for example, the text is divided into units called paragraphs to make the reading easier and interesting. Also, each paragraph starts with an indent to the right. It is done to show that a new idea or concept is being introduced in the next paragraph.
Why is a paragraph needed?
1. To make reading easier.
2. To mark an introduction of a new concept.
3. To mark a step in the development of an argument.
4. To reduce the monotony.
Important!
There is no specific unit to specify the length of a paragraph. It can be short or long, as required to explain the point.
What are the important features of a paragraph? 
1. Unity: Each paragraph should deal with a single idea or thought. If you are writing an essay, each paragraph should have a heading, and a sub-heading if required. Every sentence should be coherent and should develop the idea as it progresses. It must remain closely connected to the main idea of the paragraph.

2. Order: There should be a logical sequence followed in the expression of ideas. The topic should be relevant to the paragraph and vie-versa. There can be development of the topical idea but not a deviation. If there is a counter-argument point, it must be taken to the next paragraph. It should follow the logic of introduction in the first sentence, explanation in the middle part and the conclusion must answer all the questions raised at the start of the paragraph.

3. Variety: The paragraphs can be of varying lengths, as the case requires. It can be of one or two sentences, or even of eight sentences. Varying lengths of paragraphs add variety to the text and make it look better and easier to read.
Important!
The paragraphs should start further from the margin than the main part of the paragraph - this is called an indent.
An example of paragraphs from the lesson "A Short Monsoon Diary":
  
The first day of monsoon mist. And it’s strange how all the birds fall silent as the mist comes climbing up the hill. Perhaps that’s what makes the mist so melancholy; not only does it conceal the hills, it blankets them in silence too. Only an hour ago the trees were ringing with birdsong. And now the forest is deathly still as though it were midnight.
     Through the mist Bijju is calling to his sister. I can hear him running about on the hillside but I cannot see him.
      Some genuine early-monsoon rain, warm and humid, and not that cold high-altitude stuff we’ve been having all year. The plants seem to know it too, and the first cobra lily rears its head from the ferns as I walk up to the bank and post office.
     The mist affords a certain privacy.
     A school boy asked me to describe the hill station and valley in one sentence, and all I could say was: “A paradise that might have been.”
Reference:
National Council of Educational Research and Training (2006). Honeydew. A Short Monsoon Diary (pp. 109-117). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.