When I saw the picture I thought: ‘Wristwarmers for skeins?’ ;-)
No, it is a skein holder to prevent the skein from unraveling and rolling around when you knit it from the center.
By the way, I have presented before how to wind a center pull yarn ball :)
Links:
Skein Holder (Yarn Ball Cozy)
Here at unikatissima:
Center Pull Yarn Ball