In this video, the teacher explains how to develop well-written and cohesive paragraphs by using supporting words and phrases. They emphasize the importance of presenting related ideas and evidence in a paragraph that flows nicely and makes sense to the reader. The teacher also highlights the common mistake of simply listing evidence from an outline without ensuring cohesiveness. They provide step-by-step guidance on writing a topic sentence and using supporting phrases to create a tight and cohesive paragraph.