Dynamic stall poses a significant aerodynamic challenge for vertical axis wind turbines (VAWTs) and serves as a key impediment to enhancing their overall efficiency. Consequently, to elucidate the underlying mechanism of dynamic stall and facilitate a clearer understanding of the entire dynamic stall process, a numerical investigation is conducted over the blades of a VAWT system. A two-dimensional numerical simulation is conducted by employing unsteady Reynolds-averaged Navier-Stokes (RANS) calculations with a Reynolds stress turbulence model. Four real-time key indicators are generalized to quantitatively characterize dynamic stall over the VAWTs. These indicators have been demonstrated to accurately predict the initiation and detachment times of the dynamic stall vortex (DSV), providing deeper insights into the underlying mechanism of DSV development. Additionally, this study explores the impact of blade thickness on the dynamic stall of VAWTs. Three airfoils from the NACA 4-digit series, each featuring distinct ratios of thickness to chord length, are examined. As the blade cross-section transitions from NACA 0012 to NACA 0015 and NACA 0018, heightened blade thickness results in a delayed onset of dynamic stall, shifting from leading edge stall to trailing edge stall. Moreover, the blade thickness significantly influences the efficiency of VAWT system, with increased airfoil thickness contributing to an improved utilization of wind energy.