Surface tension is the main driver of the movement of water across fabrics.

Some materials, like cotton, are very porous, and have low "contact angle", a property which governs the wettability (yes, a real word) of the material. This encourages the ABsorption of water, both along the length of the fibers, and into every nook and cranny of a given fiber as well. This is what makes cotton so absorbent, but it's also what makes it such a terrible fabric to have against your skin. It TRAPS moisture. Once the water gets into those little nooks and crannies, surface tension keeps it there, and very little of the water is exposed to the air, so it dries very slowly.

Other materials, like nylon, are inherently non-porous, so they can't ABsorb water into the individual fibers. They can, however, still ADsorb (also a real word) water along the length of the fibers. This means that the water is just sitting in top of the fiber, fully exposed to the air, allowing it to evaporate quickly. This tends to be true of most of the synthetic fibers, which is why they dry so quickly once they DO get wet. Getting them wet in the first place, however, is hard, because they tend to have higher contact angles, which makes it harder for water to get a hold, and some of them, like nylon, can be woven so tightly that they almost become hydrophobic. This is why synthetic clothes dry really fast, but also feel nasty against your skin when you sweat - the sweat doesn't get picked up off your skin, so you just feel the sensation of water on your skin.

Now take wool. A truly impressive fiber. It's not really porous in and of itself, so it doesn't absorb very much, but it has a lower contact angle and greater ability to ADsorb water, which makes it much better and pulling water off your skin. This is why all of the finest expedition, outdoor, and sports clothes are made of merino wool. It's naturally anti-bacterial, and it's proficiency at wicking away water, and then letting it evaporate, makes it very thermo-regulating. It keeps you warm in the winter, and cool in the summer.