In this video the speaker explains the concept of circular speed of an object orbiting another body, such as a planet or moon, using mathematical formulas and derivatives. The formula for circular speed is derived and explained, and its application to real-world scenarios, such as satellites orbiting the Earth and Mars, is demonstrated. The speaker also touches on how this simple function has contributed to our understanding of dark matter in the universe. Throughout the video, the speaker provides examples and exercises to help illustrate the concepts, including a calculation of the circular speed of Mars and a discussion of the domain and range of the function.