Polycrystalline CaCu3Ti4O12 (CCTO) ceramics were prepared via a wet-chemistry method. Complex dielectric permittivity spectroscopy was performed on CCTO ceramics. We noticed that three distinct Maxwell-Wagner relaxations were clearly separated and could be associated with three mechanisms of extrinsic origins. These relaxations, which take place at three kinds of internal insulating barrier layers and at their respective frequency regions, explain the observed colossal dielectric constant at room temperature. In addition, the associated migrations of charge carriers manifest at the same frequency regions in ac conductivity spectra as the corresponding dielectric relaxations. We provided a complete and consistent scenario to elucidate the dielectric responses of CCTO and compare it with previous studies. The resistivity obtained from a semicircular arc of the impedance spectroscopy at low frequencies was interpreted as the surface resistivity instead of the grain boundary resistivity.