The first theoretical model of Fourier domain mode locking operation is presented. A specially tailored dynamic equation in a moving spectral reference frame is derived, enabling efficient numerical treatment, despite the broad laser spectrum and the extremely long cavity. The excellent agreement of the presented theory with experiment over a wide range of operation parameters enables a quantitative assessment of the relevant physical effects, such as the spectral loss modulation and gain saturation dynamics, amplified spontaneous emission, linewidth enhancement, and self-phase modulation.