Hydrogels are hydrophilic 3D networks that are able to ingest large amounts of water or biological fluids, and are potential candidates for biosensors, drug delivery vectors, energy harvester devices, and carriers or matrices for cells in tissue engineering. Natural polymers, e.g., cellulose, chitosan and starch, have excellent properties that afford fabrication of advanced hydrogel materials for biomedical applications: biodegradability, biocompatibility, non-toxicity, hydrophilicity, thermal and chemical stability, and the high capacity for swelling induced by facile synthetic modification, among other physicochemical properties. Hydrogels require variable time to reach an equilibrium swelling due to the variable diffusion rates of water sorption, capillary action, and other modalities. In this study, the nature, transport kinetics, and the role of water in the formation and structural stability of various types of hydrogels comprised of natural polymers are reviewed. Since water is an integral part of hydrogels that constitute a substantive portion of its composition, there is a need to obtain an improved understanding of the role of hydration in the structure, degree of swelling and the mechanical stability of such biomaterial hydrogels. The capacity of the polymer chains to swell in an aqueous solvent can be expressed by the rubber elasticity theory and other thermodynamic contributions; whereas the rate of water diffusion can be driven either by concentration gradient or chemical potential. An overview of fabrication strategies for various types of hydrogels is presented as well as their responsiveness to external stimuli, along with their potential utility in diverse and novel applications. This review aims to shed light on the role of hydration to the structure and function of hydrogels. In turn, this review will further contribute to the development of advanced materials, such as "injectable hydrogels" and super-adsorbents for applications in the field of environmental science and biomedicine.