Moisture transport and/or storage in clothes plays a major role on the comfort or discomfort they procure due to the resulting wetness or heat loss along the skin. Our current knowledge of these complex processes, which involve both vapor transport and water sorption in the solid structure, is limited. This is, in particular, due to the open questions concerning the sorption dynamics at a local scale (for modeling), which lead to complex nonvalidated models, and to the challenge that constitutes the direct observation of these transports (for measurements). Here, through unique experiments, we directly observe the bound-water transport in a model textile sample during drying with the help of an original magnetic resonance imaging technique. Despite the various physical effects involved, this transport appears to follow a diffusionlike process. We then demonstrate theoretically that this process is described in detail (at a local scale) by a simple model of vapor transport through the structure assuming instantaneous sorption equilibrium and without any parameter fitting, which finally brings a simple response to modeling. This, in particular, allows us to quantify, as a function of simply measurable material parameters and air-flux impact, the characteristic time during which the evaporation of sweat is accelerated by sorption, the time during which a textile constitutes a barrier against ambient humidity, or the conditions of mask humidification. These results open the way to a full characterization and prediction of fabric properties under different conditions, and to direct formulation of high-performance materials by adjusting the material constituents.