What is the difference between reptiles and amphibians in respect to their skin?

Reptiles and amphibians are both ectothermic vertebrates, so they do share a number of similarities. The question does ask about the skin, and the skin is something that both groups share, instead of one organism having skin and the other having something like an exoskeleton; however, the skin differs in form and function. Amphibian skin is, in general, very thin. Additionally, it does not provide a water tight barrier. This is why amphibians live near water. The moist environment slows down water loss and helps them re-hydrate as well. Amphibian skin is also permeable to gasses. In contrast, reptile skin is much thicker and dryer. This allows them to retain water much better than an amphibian, which in turn allows reptiles to live in much dryer environments. The outermost layer of reptile skin is composed of a covering of keratin which gives it a much harder texture than amphibian skin.
http://www.anapsid.org/basicdermatology.html