Madame Sofronie is the owner of a hair shop, which, we are told, sells "hair goods of all kinds" (12). She is "large," "white," and "chilly" (12). Her manner is direct and to-the-point: she doesn't give off any signs of being impressed by Della's gorgeous hair, and casually offers to buy it for $20.
Madame Sofronie's attitude creates a sharp contrast to that of Della and Jim. For both of them, Della's hair is a prized possession – her only prized possession – and Della's sale of it amounts to an enormous sacrifice. None of this matters to Madame Sofronie, for whom it's just another business transaction, which will perhaps fetch a bit more profit. You could say she represents "the cold, uncaring world" which exists outside the haven of love Della and Jim have built for themselves. She also represents a very different way of valuing things – purely for the money they fetch.