Orthogonal functions are a set of functions that are mathematically independent of each other, meaning their inner product equals zero. This property is similar to how perpendicular lines in geometry do not affect each other. In practical terms, if you take two orthogonal functions and integrate their product over a specific interval, the result will be zero. These functions are essential in various fields, including signal processing, quantum mechanics, and Fourier analysis. In Fourier analysis, for example, orthogonal functions help decompose complex signals into simpler components, making it easier to analyze and manipulate data.