A Taylor series is a mathematical representation of a function as an infinite sum of terms calculated from the function's derivatives at a single point. It allows us to approximate complex functions using polynomials, making them easier to analyze and compute. The series is centered around a specific point, often denoted as a, and each term involves the function's derivatives evaluated at that point. The general formula for a Taylor series is given by f(x) = f(a) + f'(a)(x-a) + \fracf''(a)2!(x-a)^2 + \ldots. This series converges to the function within a certain interval around the point a, providing a powerful tool in calculus and mathematical analysis.