Taylor's theorem is a fundamental concept in calculus that provides a way to approximate a function using polynomials. It states that any smooth function can be expressed as an infinite sum of terms calculated from the function's derivatives at a single point. This means that if you know the function's value and its derivatives at a specific point, you can create a polynomial that closely resembles the function near that point. The theorem is often used in mathematical analysis and numerical methods to simplify complex functions. The polynomial created from Taylor's theorem is called a Taylor series, and it can be truncated to a finite number of terms for practical calculations, allowing for easier computation and analysis of functions.