Describes textiles when the pile or nap is so worn the base canvas threads show through. Threadbare floor rugs which have seen time are relatively inexpensive, and generally still have 20-30 years of life left in them–for me, they are far more attractive than a carpet with a plush, high pile, and perfect for rural and country chic environments. The colours tend to be softer, muted, showing that they have contended with the ravages of hard wear, tear and sunlight.
Threadbare sofa arms are also acceptable to my mind, even with small holes–so long as the original fabric was of good quality, it can stand a bit of wear and fraying. Covering these up tastefully with patches or new arm covers is a perfectly OK solution.