Fe3+- or Nb5+-doped CaCu3Ti4O12 (CCTO) ceramics show higher values of both room-temperature (RT) grain conductivity and dielectric constant than undoped ceramics. Microstructural and structural characterization combined with magnetic properties reveal the coexistence of two components that seem relevant for the dielectric behavior of the material. The grain possesses a nanostructure characterized by layered domains with thicknesses <80 nm. The formation of the layered domains is associated with the evidence of different chemical states as Cu2+/Cu+ and Ti4+/Ti3+ that are present in the material. The magnetic contribution is related to two coupled effects: the antiferromagnetic (AFM) response with TN=25 K ascribed to Cu2+, and a paramagnetic-like contribution attributed to Ti3+ cations. The coexistence of two coupled magnetic contributions could explain the proposed unusual coupling of the AFM Cu2+ superexchange interaction through the nonmagnetic Ti4+ rather than via the usual oxygen coupling. The lower the paramagnetic-like contribution at RT, the larger the conductivity and the dielectric constant of the material are. Below 150 K, the increase of the paramagnetic-like contribution is correlated with the low transition temperature of the CCTO.