Linear polarimetric transformations of light polarization states by the action of material media are fully characterized by corresponding Mueller matrices, which contain, in an implicit and intricate manner, all measurable information on such transformations. The general characterization of Mueller matrices relies on the positive semi-definiteness of the associated coherency matrix, which can be mathematically formulated through the nonnegativity of its eigenvalues. The enormously involved explicit algebraic form of such formulation prevents its interpretation in terms of simple physical conditions. In this work, a general and simple characterization of Mueller matrices, based on their statistical structure, is presented. The concepts associated with the retardance, enpolarization, and depolarization properties as well as the essential coupling between the latter two are straightforwardly described in the light of the new approach.