Fabric texture is the feel of the fabric. It can be smooth, rough, soft, velvetty, silky, lustrous, and so on. The different textures of the fabric depends upon the type of weaves. 
The type of texture sets the mood of the wearer. Rough textured fabrics say "picnics," where as soft textured fabrics whisper for "formal dinners." Cotton damask, toile having sheer linen and silk cloth, chints, and soft chenille speak of formal and traditional spaces.
Textures are given to all types of fabrics, cotton, silk, wool, leather, and also to linen. Few of the famous fabric textures are flannel, velvet, organdy, chintz, crepe, damask, challis, venise, suede and embossed leather.