The first secant line, a fundamental concept in differential calculus, approximates the slope of a function at a given point. It connects two points on the curve and its slope is calculated as the difference in function values divided by the difference in input values. The first secant line provides an initial approximation of the instantaneous rate of change, which is formally defined as the derivative. Understanding the first secant line is crucial for grasping the concept of derivatives and their applications in calculus.