This is a sewing kit. It has a little hook so it can hang on the skirt.
From what can be seen of the clothes, it is probably of the edwardian era, if indeed the sewing kit and the clothes are related at all - the source blog doesn’t specify any dates.
This kind of sewing kit would be worn on sundays, and is mostly viewed as ceremonial jewelry, since there’s no working on a sunday. But it would come in handy should a seam be loose since it could then be remedied immediately. (I suppose they don’t count that as working on a sunday, then?)