What does it mean when a child's hands peel for no obvious reason?

Sweat problem. Sometimes hands will peel as a result of a sweet gland problem called dishydrosis. If the fingertips alone are peeling, that is common with strep throat and it is recommended to be tested for strep. Sometimes contact dermatitis (touching something one is allergic to) can lead to peeling. This question is best helped with a visit to be properly evaluated.