Anything that's woven is made by braiding or intertwining threads or fibers. Your beautiful woven blanket is extra special because it was made by hand from local wool.
A woven basket is made by interlacing strips of a material — dried grasses, straw, thread, or wood, for example — usually forming a circular base and solid sides. When something is woven, it has a solid form despite its seemingly fragile parts. A heavy woven rug started as individual wool fibers that had to be interlaced to form the thick mat beneath your feet.