A validated numerical model developed for the study of helium barrier discharges in the presence of dry air impurities is presented in this paper. The model was used to numerically investigate the influence of air traces on the evolution of the helium dielectric barrier discharge (DBD). The level of dry air used as impurity was in the range from 0 to 1500 ppm, which corresponds to the most commonly encountered range in atmospheric pressure discharge experiments. The results presented in this study clearly show that the plasma chemistry and consequently the discharge evolution is highly affected by the concentration level of impurities in the mixture. In particular, it was observed that air traces assist the discharge ignition at low concentration levels (~55 ppm), while on the other hand, they increase the burning voltage at higher concentration levels (~1000 ppm). Furthermore, it was found that the discharge symmetry during the voltage cycle highly depends on the concentration of air. For the interpretation of the results, a detailed analysis of the processes that occur in the discharge gap is performed and the main reaction pathways of ion production are described. Thanks to this approach, useful insight into the physics behind the evolution of the discharge is obtained.