What does the craving of chewing ice mean? It can be a form of stress relief. Sometimes it's just a habit.
It also can, but not always, be linked to iron deficiency anemia. It's a symptom of anemia not a cause. So you might want to have your blood iron levels checked. It's a form of pica where you crave non food items. Be grateful it's not dirt, chalk, paper or laundry soap. Low iron is more common in women. Vit C will help you absorb more iron as long as there isn't a primary concern - ie pregnancy, blood loss, ulcer, colon cancer, or other iron deficiency problem. If you have a serious deficiency (ie ulcer or colon cancer) sometimes it's linked with a burning tongue or mouth sensation. However, not all burning mouth syndromes are linked to iron deficiency.
If you're healthy, then the only damage you are doing is to your teeth. Ice can crack fillings or chip porcelain off crowns. Non-effected teeth or teeth with no fillings have less of a risk. If you have sealants, ice can break those off too. As a Utah Family Dentist, we will not recommend chewing ice. If you cannot get rid of the craving, at least switch to the soft balled ice, hospital, or "Sonic" ice. It's less dense and will cause less damage.