Dynamics and instability of a vortex ring impinging on a wall were investigated by means of large eddy simulation for two vortex core thicknesses corresponding to thin and thick vortex rings. Various fundamental mechanisms dictating the flow behaviors, such as evolution of vortical structures, formation of vortices wrapping around vortex rings, instability and breakdown of vortex rings, and transition from laminar to turbulent state, have been studied systematically. The evolution of vortical structures is elucidated and the formation of the loop-like and hair-pin vortices wrapping around the vortex rings (called briefly wrapping vortices) is clarified. Analysis of the enstrophy of wrapping vortices and turbulent kinetic energy (TKE) in flow field indicates that the formation and evolution of wrapping vortices are closely associated with the flow transition to turbulent state. It is found that the temporal development of wrapping vortices and the growth rate of axial flow generated around the circumference of the core region for the thin ring are faster than those for the thick ring. The azimuthal instabilities of primary and secondary vortex rings are analyzed and the development of modal energies is investigated to reveal the flow transition to turbulent state. The modal energy decay follows a characteristic −5/3 power law, indicating that the vortical flow has become turbulence. Moreover, it is identified that the TKE with a major contribution of the azimuthal component is mainly distributed in the core region of vortex rings. The results obtained in this study provide physical insight of the mechanisms relevant to the vortical flow evolution from laminar to turbulent state.