This is called Aquagenic Wrinkling of the Palms. I had this exact same condition on my palms, and so did my little sister. The solution is simple!! I did some research and found out that Drysol (typically used under the arms as an anti-persperant) works to get rid of this. You can find it at any drugstore...and fyi if you have very sweaty underarms it's a miracle drug. Just apply Drysol to your palms before bed, and within a day or two the condition should clear up! I did this and told my sister to as well and we haven't had a problem since. No idea why it works but it does!
Hi
This may be due to frequent hand washing, dry skin or dehydration. I would suggest that you refrain from prolonged handwashing . This may not be something serious. Wash the hands using a mild cleanser. Moisturize the hands using a mild and light vitamin E cream to keep it from drying. Drink plenty of water and avoid exposing the hands to chemicals and substances that may cause drying of skin.