Cyclic yaw control shows significant potential to enhance wind farm power performance, with prior studies demonstrating power gains exceeding 30%. However, the underlying flow mechanisms responsible for these improvements remain poorly understood. This study elucidates these mechanisms by performing stereoscopic particle image velocimetry measurements of turbine wakes under different control parameters (i.e., yaw amplitude and Strouhal number, St) and inflow conditions. Systematic investigation reveals how CYC significantly modifies wake characteristics in ways that depend on both the control parameters (especially St) and the background flow turbulence. In general, at relatively low St, CYC enhances wake meandering, which increases flow entrainment, wake expansion and, ultimately, farm power production. The optimum St is found to be smaller for longer wind farms as CYC generates larger-scale meandering motions that can persist further downstream. Conversely, at high St, these effects diminish rapidly along the streamwise direction, making CYC ineffective. The impact of CYC decreases when the inflow turbulence intensity or the integral length scale increases, owing to the more dominant role of ambient turbulence on wake meandering. Although CYC only deflects the wake laterally, it also modifies the interactions with the upper flow, leading to an increase in the mean kinetic energy entrainment and a reduction of the vertical wake width. Overall, our findings provide critical insights into how control parameters and inflow conditions govern wake flow and power performance, delivering essential knowledge for designing effective wind farm control strategies.