Fabric or cloth was a material of natural or artificial origin which was mainly used for creating clothing and protective creations such as blankets or curtains.
The Talosians of Talos IV and one of their specimens, Vina, wore garments made of metal fabric. (TOS: "The Cage")
In 2268, Sylvia told "William Claiborne" that she planned to make a gown out of several yards of a "scrumptious material" she'd bought. (TOS: "Spectre of the Gun")
While Beverly and Wesley Crusher were shopping at the mall of Farpoint Station in 2364, they witnessed how the fabric of one of the Bandi shopkeepers changed to please Beverly as she said before. As a result she purchased the entire bolt and had it sent up to the USS Enterprise. (TNG: "Encounter at Farpoint")
Under the influence of a polywater intoxication, Natasha Yar placed several pieces of fabric over her body in front of the mirror in her quarters when Deanna Troi entered. (TNG: "The Naked Now")
Retaya was a Flaxian assassin who posed as a merchant dealing in fine fabrics and perfumes. (DS9: "Improbable Cause")
A napkin was a piece of fabric. (DS9: "Hard Time", "Blaze of Glory")