Moisture wicking works in a way similar to that of a candle wick, from which the "wicking" process gets its name. A candle wick absorbs wax and draws it up toward the flame, and in the same way, moisture-wicking fabrics pull moisture away from the body and through to the outside of the fabric, where it can evaporate more easily.
According to HowStuffWorks, moisture-wicking fabrics are a product of modern technology. Modern polyester blends don't retain moisture as natural fabrics do, only holding on to approximately 0.4 percent of the moisture they experience. As a result, the person wearing the fabric feels dry even when sweating. Wicking fabrics are woven so as to be highly permeable, so that moisture finds an easy way through the fabric to the outside. Some wicking fabrics are also chemically treated to keep from retaining moisture.
According to Slate, some people have expressed concern that moisture-wicking fabrics disrupt the body's use of sweat as a natural cooling mechanism. If the body does not cool properly, there is a chance that it could sweat even more, producing dehydration. However, studies on the heat effects of working out while wearing moisture-wicking fabric show that the garments don't have a demonstrable effect on core body temperature.