Orthogonal polynomials are a special set of polynomials that are orthogonal to each other with respect to a specific inner product. This means that the integral of the product of any two different polynomials in the set over a certain interval equals zero. They are often used in various fields such as mathematics, physics, and engineering for solving problems involving approximation and numerical analysis. Common examples of orthogonal polynomials include Legendre polynomials, Chebyshev polynomials, and Hermite polynomials. These polynomials have important properties that make them useful for tasks like function approximation and spectral methods in numerical solutions of differential equations. Their orthogonality helps in simplifying calculations and improving accuracy in various applications.