There are two main types of fabrics: natural and synthetic. Natural fabrics such as wool, cotton, silk, and linen are made from animal coats, cotton-plant seed pods, fibers from silkworms, and flax (fiber from the stalk of a plant), respectively. Synthetic fabrics such as nylon,spandex, rayon, polyester, and acrylic are man-made. These fabrics differ in a number of ways, such as:
1. Warmth: Wool is particularly warm because the fibers have little crimps in them. These create pockets of air in the material that help to insulate.
2. Breathability: Cotton "breathes", which means when used as clothing it allows air to circulate to your skin. Many people prefer 100% cotton to polyester blends because of the breathability factor.
3.Strength: Linen, spandex, and polyester are all quite strong and durable.
4. Dying Properties: Linen, for example, is a good fabric to dye because the color sets well and won't fade much.
5. Softness / Scratchiness: Many type of wool, of course, are quite itchy (due to the crimps in the fibers), and cotton and silk are known for their softness.
6. Properties when wet: "Absorbent" cotton will retain 24-27 times its own weight in water and is stronger when wet than dry.
7. Luster (shininess): This property is what makes silk so desirable. Rayon is a man-made substitute than can look similar.
8. Elasticity: A lot of the synthetic fibers are very elastic. This means you can stretch them and they will "bounce back" to their original shape. Spandex was developed with this property in mind. Nylon, which is used in hosiery, is also very stretchy.

Fabrics are made of fibers - strands that are much longer than they are wide and generally round on cross section. These fibers may be from natural or synthetic sources. Humans originally made cloth from natural sources, but have subsequently found the means to make their own fibers starting from basic chemicals. Each type has different properties of flexibility, ability to serve as insulation, ability to conduct moisture.

Natural Fibers:
Wool - From sheep most commonly, but also from a host of other animals including Llamas, vicunas, alpacas, horses, camels, etc. Good insulation, flexibility, may resist wetting.

Cotton - From the fibers of the seed pod of the cotton plant, Gossypium. Good flexibility, wearing qualities. transmits water.

Linen - From the fibers of the stem of the flax plant, Linum. Heavier than cotton, but still flexible. Excellent wearing characteristics. Transmits water.

Jute From the surficial fibers of a small tree of the Linden family, Cochorus. Very tough, rough, not too flexible. Often more for rope, but may be made into cloth.

Hemp - From the stem fibers of Cannabis.

As for Jute.
Tapa - from the bark fibers of Broussonetia. Soft, but not very flexible. Rare in western culture.

Cotton and Linen are by far the most widely used.

And there are a LOT more. Seek out a text on Economic Botany and consult the chapter on "cloth" if you want to learn about them.

More recently, humans have learned to make their own fibers, primarily from two sources. First, by dissolving the cellulose found in the cell walls of plants and then re-forming it into thread. This is the source of Rayon. Since cellulose is the primary constituent of all but the wool fibers noted above, we are just re-inventing the wheel.

Second, by synthesizing cellulose-like molecules from oil. By example, Nylon, polyester.

The synthetic forms tend to be quite flexible, but often are very poor at "breathing", that is, letting body heat and sweat out. Hence they are often mixed with cotton.