In this video, the teacher explains how to write a strong concluding paragraph for an argumentative essay. They emphasize the importance of summarizing the main points, restating the thesis, and providing a call to action. The teacher also highlights common mistakes to avoid, such as leaving the argument unfinished or not convincing the reader of the argument's validity. By following their step-by-step guidance, students can create a well-written conclusion that leaves a lasting impact on the reader.