Viscose is a type of rayon. It is a fiber made of regenerated cellulose...from green plants. It's structurally similar to cotton but is be produced from a variety of plants such as soy, bamboo, and sugar cane.
It's been called a contradictory beast because as a manufactured fiber, it's neither truly natural like cotton, wool or silk nor truly synthetic like nylon or polyester. It's somewhere "in between".
Viscose became popular for a few reasons. The first is that it has a luxurious look and feel at an affordable price. It blends easily with other fibers. It is easy to dye and retains vivid colors very well. It's got a silk-like luster, nice drape and is softer than cotton.
It's often blended with other fabrics - like polyester.