What does it mean when your hands and feet peel with little round empty blisters?

Could be any number : Of things. You should see your primary care doctor or a dermatologist and let them check it out.

Dyshidrotic eczema: This is probably a condition called dyshidrotic eczema. This can be treated with steroid creams or ointments applied to the area with the blisters. Other treatments for resistant cases include phototherapy, and creams that suppress an over-active immune system in the affected skin. You can find more information here: http://www.Nlm.Nih.Gov/medlineplus/ency/article/000832.Htm.