In this paper, we investigated the tetrahedral structure of supercooled water at ambient pressure and its influence on dynamic relaxation by comparing simulation results of TIP4P/2005 and SPC/E water models. The globally tetrahedral structure of supercooled water was characterized with the second-peak maximum and a deep first minimum in the radial distribution function g(r) of O-atoms and the reverse order in magnitude between the first two peaks of structure factor. The locally tetrahedral structure was specified by molecules, which and their neighbors up to the second hydration shell all have four H-bond coordinators. These molecules are referred as low-density liquid (LDL) and the others as high-density liquid (HDL). The water dynamics relaxation was studied through the self-intermediate scattering function, the non-Gaussian parameter, and the polarizability anisotropy time correlation function. Indicated by our simulations, the temperature dependence of the stretched exponent describing the α-relaxation displayed a small peak in the supercooled regime above the Widom line (WL), where LDL at the peak temperature was roughly one fourth of the total. The stretched exponent depicting the polarizability anisotropy relaxation was found to be insensitive to temperature, consistent with the experimental results. Above the WL, all relaxation times studied displayed a power-law temperature dependence with a consistent singular temperature for each model. The inverse relaxation times showed exponential functions of two-body excess entropy due to translational motions, where the entropy exhibited a logarithmic temperature behavior with a singular temperature close to that of relaxation time. This result leads to a conclusion that excess entropy is a quantity to describe dynamic relaxation of supercooled water in the thermodynamic region where the mode-coupling theory works. The water structure that causes the two-body excess entropy is illustrated and the contributions of HDL, LDL, and their mixing are also shown, where the mixing contributes significantly as near the WL. Below the WL, the formula based on the two-body excess entropy may no longer be valid.