The periodic synthetic jet emerging from a circular hole actively controls the turbulent boundary layer (TBL). A time-resolved particle image velocimetry (TR-PIV) system was designed to capture the velocity field database and based on the single-pixel ensemble correlation (SPEC) algorithm, an average drag reduction rate of 6.2% was obtained. The results show that the synthetic jet causes a wide range of low momentum zones and a low-speed streak in the downstream flow field. And the places where the disturbance intensity is strong are often accompanied by a larger velocity deficit. The instantaneous flow fields are visualized with the Finite-Time Lyapunov Exponent (FTLE), and the hairpin vortex packet composed of five hairpin vortices and the generation of new hairpin vortices are observed when there is no control. Under the action of the synthetic jet, the hairpin vortices are continuously generated from the jet hole. The synthetic jet mainly achieves the drag reduction effect mainly by modulating the mean convection term and the spatial development term . The drag reduction effect appears in the region of x/δ0>0.38, and the maximum drag reduction rate is 12.2% at x/δ0=0.75, and then gradually decreased. Using proper orthogonal decomposition (POD), it is found that the synthetic jet reduces the energy proportion of the large-scale energetic structures. After the conditional average, the synthetic jet limits the influence range of bursting events at various scales in the near-wall region, and weakens the normal transport of momentum and energy brought about by large-scale ejection events (Q2 events) and the wall friction resistance caused by large-scale sweep events (Q4 events).