The video discusses the concept of slope in mathematics, describing it as the rate of change of a vertical variable with respect to a horizontal variable. Slope is calculated as the change in y over the change in x, often referred to as rise over run. For a line, slope remains constant regardless of the points chosen for calculation. Calculus introduces the idea of instantaneous rate of change, allowing for the analysis of curves with varying rates of change. While traditional tools yield the average rate of change between two points as the slope of the connecting line (secant line), the slope changes when different points are selected along the curve. This demonstrates the dynamic nature of rates of change and sets the stage for exploring more complex questions in calculus.