Hydration shell dynamics plays a critical role in protein folding and biochemical activity and has thus been actively studied through a broad range of techniques. While all observations concur with a slowdown of water dynamics relative to the bulk, the magnitude and molecular origin of this retardation remain unclear. Via numerical simulations and theoretical modeling, we establish a molecular description of protein hydration dynamics and identify the key protein features that govern it. Through detailed microscopic mapping of the water reorientation and hydrogen-bond (HB) dynamics around lysozyme, we first determine that 80% of the hydration layer waters experience a moderate slowdown factor of similar to 2-3, while the slower residual population is distributed along a power-law tail, in quantitative agreement with recent NMR results. We then establish that the water reorientation mechanism at the protein interface is dominated by large angular jumps similar to the bulk situation. A theoretical extended jump model is shown to provide the first rigorous determination of the two key contributions to the observed slowdown: a topological excluded-volume factor resulting from the local protein geometry, which governs the dynamics of the fastest 80% of the waters, and a free energetic factor arising from the water protein HB strength, which is especially important for the remaining waters in confined sites at the protein interface. These simple local factors are shown to provide a nearly quantitative description of the hydration shell dynamics.