The Eddington Approximation is a well-defined, relatively-easy-to-work-with description of Electromagnetic Radiation's variation by direction (departure from isotropic), used in modeling Stellar Structure. Assuming Isotropy could make modeling even simpler, but would fail to transfer energy toward the surface where it is emitted as starlight. The Eddington approximation assumes there is a general transfer of energy away from the middle of the star ("up"), and models the Intensity of radiation in each direction such as to do that, with minimal complication of the equations. It is one of the approximations developed to make the modeling of stars practical.
Equation of Radiative Transfer (RTE)