These "Stress balls" or "Baoding balls" are a Chinese invention going back to Antiquity. They can be found constructed of virtually any material from plain carved bone to elaborate cloisonne. What these large "Marbles" are usually used for is exercise and meditation, but are they are also employed for medical reasons. To use them for exercise, one places two Baoding balls within their palm then rotate them clockwise and counterclockwise and keeping them from touching Alternative Medicine advocates believe that the balls are beneficial for medical reasons when they touch pressure points or acupuncture points found all over the hand.
Values for most of these balls are very modest, as they've never really been out of production and are still made today. Boxed sets like the one shown are of fairly modern construction and are still available for less than $30.00. Values for rare early jade examples are an exception, often going at auction for $400.00+ a pair