Simulations of water near extended hydrophobic spherical solutes have revealed the presence of a region of depleted density and accompanying enhanced density fluctuations. The physical origin of both phenomena has remained somewhat obscure. We investigate these effects employing a mesoscopic binding potential analysis, classical density functional theory (DFT) calculations for a simple Lennard-Jones solvent, and Grand Canonical Monte Carlo (GCMC) simulations of a monatomic water (mw) model. We argue that the density depletion and enhanced fluctuations are near-critical phenomena. Specifically, we show that they can be viewed as remnants of the critical drying surface phase transition that occurs at bulk liquid-vapor coexistence in the macroscopic planar limit, i.e., as the solute radius Rs → ∞. Focusing on the radial density profile ρ(r) and a sensitive spatial measure of fluctuations, the local compressibility profile χ(r), our binding potential analysis provides explicit predictions for the manner in which the key features of ρ(r) and χ(r) scale with Rs, the strength of solute-water attraction ɛsf, and the deviation from liquid-vapor coexistence of the chemical potential, δμ. These scaling predictions are confirmed by our DFT calculations and GCMC simulations. As such, our theory provides a firm basis for understanding the physics of hydrophobic solvation.