The "wicking" method, also called "the training wheels of the hydroponic world," is the most beginner friendly hydroponic system. In this system, capillary action, the mechanism which allows towels to draw liquid from the surface, carries the nutritient solution to the root area of the plant.
In other words, you know when you accidently sit on a wet surface and your clothes get wet? Depending on the cloth, it doesn't stay wet in one place. Often times it spreads. If it's enough water and absorbing fabric, it spreads up. In this case, the water you sat on is the nutrient solution. Your clothes are the wick. The spreading is capillary action, taking the nutrients up to your root zone (wherever that may be).