The answer lies in the basic but remarkable molecular structure of cotton, synthetic fibers and water. The simple water molecule, with its one oxygen atom attached to two hydrogen atoms, causes a different action when it comes in contact with the complex molecules that make up cotton and synthetic fibers. read more
Refer to Asad answer about swelling and structure of the Cotton fibre for the absorbancy aspect. This is why cotton is so good for towelling etc. In the case of synthetics they all have some absorbancy, generally Polyester is hydrophobic so does not like water but there is a small degree of absorbancy there. read more
(Synthetic fibers like nylon are solid, with no internal spaces within the fiber to contain water. Whatever water is absorbed is contained on the fibers’ surfaces.) Lumens also radically increase the surface area of the fiber for water to interact with, which leads to the chemistry part of this. Processed cotton fibers are 99 percent cellulose. read more