The epsilon-delta definition is a formal way to describe the concept of limits in calculus. It states that for a function to approach a limit as the input approaches a certain value, we can make the output as close as desired to the limit by choosing inputs sufficiently close to that value. Here, epsilon (ε) represents how close we want the output to be, while delta (δ) represents how close the input must be to the target value. This definition is crucial for understanding continuity and differentiability in mathematics. It was introduced by the mathematician Augustin-Louis Cauchy and later formalized by Karl Weierstrass. The epsilon-delta approach provides a rigorous foundation for analyzing the behavior of functions as they approach specific points.