This paper proposes a polaronic stacking fault defect model as the origin of the huge dielectric properties in CaCu3Ti4O12 (CCTO) materials. The model reconciles the opposing views of researchers on both sides of the intrinsic versus extrinsic debate about the origin of the unusually high values of the dielectric constant measured for CCTO in its various forms. Therefore, by considering stacking fault as the origin of the high dielectric constant phenomena, it was shown that the internal barrier layer capacitance mechanism is enhanced by another similar, but different in nature, mechanism that operates in the nanoscale range due to polaron defects associated with stacking fault, a mechanism that was referred to as nanoscale barrier layer capacitance (NBLC). The NBLC approach explains the origin of the CCTO's huge dielectric constant coexisting with semiconducting features.