Chebyshev approximation is a mathematical technique used to find the best approximation of a function by a simpler one, typically a polynomial. It minimizes the maximum error between the function and its approximation over a specific interval, ensuring that the approximation is as close as possible to the original function at all points. This method is based on Chebyshev polynomials, which are a sequence of orthogonal polynomials that play a crucial role in this approximation process. By using these polynomials, mathematicians can create more accurate models for complex functions, making Chebyshev approximation valuable in fields like numerical analysis and engineering.