We present experimental data on the conductivity evolution in InOx nanocrystalline (nano-grained) films after UV light irradiation, and its dependence on film thickness. These experimental data are indicative of new irradiation-induced effects in the nanocrystalline matter and used as input in elaboration of a theoretical model describing physical mechanisms of the UV light irradiation-induced enhancement of the conductivity in nanocrystalline films. In the framework of the model, the experimentally detected peculiarities of InOx nanocrystalline films are attributed to the presence of high-density ensembles of grain boundaries in such films. In particular, the enhancement of conductivity in these films is theoretically described as a phenomenon related to irradiation-induced structural transformations of grain boundaries and ionization, whose intensities are highly sensitive to the film thickness.