We present a theoretical study for ion hydration based on an integral equation method referred to as the extended reference interaction site method (ex-RISM). We analyze the thermodynamic functions of solvation, especially the partial molar volumes of individual ions at infinite dilution. Special attention is paid to information contained in the partial molar volumes and to the question of whether the partial molar volumes of individual ions reflect the true nature of ion-water interactions. Our results suggest, contrary to the previous work given by Kusalik and Patey (J. Chem. Phys. 1988, 89, 5843), that the partial molar volumes do reflect the nature of ion-water interactions. Concerning the microscopic description of the ion hydration, we revisit the earlier model proposed by Samoilov by defining the activation energy Delta E-i in his model in terms of the ion-water potential of mean force. The theoretical results are in good accord with the earlier model in terms of the classification of ions into the "positive" and "negative" hydrations. We also discuss the structural changes of water due to the presence of an ion utilizing the density derivatives of the solvent distribution functions. Qualitative differences of the density derivatives between the "positively" and "negatively" hydrated ions were observed and found to be consistent with the analysis of the potential of mean force.