It's someone who sells cushions and stuffing and webbing and other materials used in making 'upholstered' (roughly, soft) furniture. Upholstery retailers are specialists, largely driven into extinction by shops that sell new furniture; they provide a service that is nearly a thing of the past - I have used such a service only about six times in my life (that's an average of once every ten years) - so in many parts of the world they may be unheard of.
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