Herein, we show that scanning probe microscopy (SPM) is an effective tool permitting to disclose the nature of the colossal dielectric permittivity characteristic of CaCu3Ti4O12 (CCTO) compound. SPM data confirm the existence of micro- and nanoscale barrier layer capacitance mechanisms which simultaneously contribute to the electrical conductivity of the material. The former mechanism is associated with the potential grain-to-grain barriers. The latter mechanism involves the barriers created by intragrain structural defects. The results of the SPM study shed new light on the origin of the colossal dielectric constant in CCTO.