Spinning skill is used to spin cotton into string, which is needed to string fishing poles, bows, and crossbows. You can also sell string at a Provisioner Shop.
To spin string, you must stand next to a spinning wheel. Double-click on the cotton, and then select the spinning wheel.
After 6 seconds you'll be told whether you’ve successfully spun the cotton into string, or destroyed it. The odds of successfully spinning cotton equals 57% + (Spinning Skill / 2) + (Dexterity / 6). A ball of string is worth 20, so you’ll get about 10 if you sell it at the Provisioner Shop.