Natural fabrics are made of fiber that either comes from an animal (hair, fur, and feathers), a vegetable (such as cotton or hemp), or a mineral (i.e. fiberglass). Fabric making can be dated back to over 10,000 years ago with the use of flax, a type of linnen, in ancient societies.
During the early twentieth century, scientists developed a new type of textile using the natural cellulose fibers from plants and petrochemicals to make Rayon. The first truely synthetic textile was Nylon. Nylon, invented in 1930, was very influental during World War II as well as post war times.
Today Synthetic Fabrics are being developed based on their use. This type of textile is incredibly important in high tensile strength rope, and multiclimate suits for soldiers.
You may be asking yourself, "What does Fabric have to do with Chemistry?" Each aspect of manufacturing successful textiles involves some kind of chemical process. Synthetic fibers are refined from pertrochemicals and then drawn into thread through a process called melt spinning.
All synthetic textiles start in a molten liquid form. That liquid is then forced through a spinnerete, which resembles a showerhead with hundreds of tiny holes. The liquid synthetic fabric strings are then cooled and dried, before they can be woven into textiles.
Both Natural and Synthetic fabrics go through a cleaning and bleaching process. Ionized soaps that are easily water solouable are used to pull impurities away from the fiber strands. The picture above shows a bleach molecule during its cleaning transformation. While some chemicals are added to the fabric to offer texture and color qualities. A popular chemical additive for clothes is Flame Retardant. Many synthetic fabrics, such as nylon, pose a great threat for fire injury. The development of this chemical was key in the safe consumer use of synthetic textiles.
Another fabric production process is dying. Dyes must be non-water soluable, as to not wash out when they are being washed. By creating a pygmented long lipid chain the fabric can be colorful as well as well-wearing.
For more on Fabric Chemistry, see the above links