The promising class of the environment-friendly thermoelectrics is the copper-based argyrodite-type ion-conducting crystals exhibiting just extraordinary low thermal conductivity below the glass limit associated with the molten copper sublattice leading to a softening of phonon modes. To explain why the argyrodite structure containing copper ions favors the low thermal conductivity, we have utilized the ab initio calculations of the electron, phonon, and thermoelectric properties of Cu7PS6 crystal in the framework of the density functional and Boltzmann transport theories. To obtain the reliable thermoelectric properties of Cu7PS6, we take into account the dependence of the electron effective mass m* on the redundant carrier concentration n. We propose to use the Burstein-Moss effect for the calculation of the electron effective mass m* of a semiconductor. We have found the strong nonlinear character of copper atom vibrations in Cu7PS6 which exceeds substantially the similar values for phosphorous and sulfur atoms. The large vibration nonlinearity of the copper atoms found in Cu7PS6 explains the diffusion-like heat transfer and the relatively low coefficient of the lattice thermal conductivity (κ = 0.7 W/(m⋅K)), which is favorable to achieve the large thermoelectric figure of merit.