Many important issues of power system dynamics are often studied by looking at the dynamic responses of generators connected through the power grid, taking their interactions into consideration. In this paper, we present a specific study on the significant impact of grid structure on the power system dynamics with quantitative evidence. Specifically, it is found that the impact of grid structure heavily depends on two types of grid-structure-related variables: 1) electrical distances among the generator internal buses, and 2) electrical distances between the generator internal buses and the faulted bus. Furthermore, with the examples of coherency identification problem, the significance of grid structure is demonstrated by the strong agreement of identification results between using a set of criteria that only takes into account the grid-structure-related variables and dynamic simulations.