A harmonic function is a type of mathematical function that satisfies Laplace's equation, meaning it is twice continuously differentiable and its Laplacian is zero. These functions are often found in various fields such as physics, engineering, and mathematics, particularly in the study of potential theory and fluid dynamics. Harmonic functions have the property of being smooth and exhibiting no local maxima or minima within a given domain, except at the boundaries. They are closely related to concepts like Fourier series and complex analysis, where they play a crucial role in understanding wave behavior and heat distribution.