Fourier coefficients are numerical values that represent the amplitude of specific frequency components in a periodic function. They are derived from the Fourier series, which breaks down complex periodic signals into simpler sine and cosine waves. Each coefficient corresponds to a particular frequency, allowing us to reconstruct the original function by summing these waves. These coefficients are calculated using integrals over one period of the function. The first coefficient, known as the DC component, represents the average value of the function, while subsequent coefficients capture the contributions of higher frequencies. This process is fundamental in fields like signal processing and harmonic analysis.