Instability ? Have you injured it? Weakness of the muscles, laxity of the tendons and ligaments or bone spurs can all cause a "popping" sound while moving your wrist. Questions would be, does it cause pain or is it weak? Any of these see your physician or Orthopedic Surgeon. If not, try exercising the wrist.Start slow and increase your exercise as tolerated. Need help, contact a physical therapist. Good luck.
Popping Wrist. This could be happing for several reasons. It could be like your knuckles cracking. You could have fluid in your joint from arthritis or some other disease. You could have an infection or it could be the results off an injury. You gave little information, so the best thing is to go to your doctor and get it evaluated.
No one knows. It's not clear why joints crack & pop. There's no clear evidence that popping joints alone is a problem if the joint is otherwise normal.http://en.wikipedia.org/wiki/Cracking_joints If you have pain or weakness along with the popping that's another story & you need to get it checked out. Here's another interesting page by the Lib. of Congress http://www.loc.gov/rr/scitech/mysteries/joint.html.