In this video, the teacher explains how to organize and develop supporting reasons for an opinion essay using the technique of boxes and bullets. The teacher emphasizes the importance of strong reasons that support the thesis statement. They provide an example of a thesis statement ("turtles are the best pets") and discuss how each reason should be a different explanation of why this is important or true. The teacher also highlights the need to avoid repetition and to extend reasons by providing experiences, facts, or details. The process of developing reasons is described, which involves writing the reason in a box, brainstorming examples that support it, and listing them as bullets. Additionally, the teacher suggests considering facts that support the claim and listing them as bullets.