In the Ohmic discharge at the TEXTOR tokamak, improved plasma confinement (reduced particle losses) have been achieved during the operation of an m/n=6/2 resonant magnetic perturbation. We have investigated the influence of the perturbation field on multi-scale turbulence and turbulent transport across the perturbation-induced improvement of plasma confinement. The results indicate that with magnetic perturbation (MP), both the large-scale zonal flows and small-scale drift-wave turbulence are significantly reduced. At high MP currents, a reduction of edge transport can be realized due to primarily the decline of small scale ambient turbulence and turbulent transport in the ergodic zone, where the turbulence eddy size is largely decreased. Investigation on the dynamic process of fluctuation quantities during the perturbation current ramp-up phase further shows that geodesic acoustic mode zonal flows and their nonlinear interaction with background turbulence decrease incessantly with increasing perturbation current. The improved confinement takes place only after small-scale turbulence starts to be strongly reduced by the MP when the MP strength reaches a certain threshold value.