Cutaneous (skin) breathing

Krishna: Mechanisms of respiratory exchange in Amphibia are remarkable for the taxa as a whole and may occur via four routes: branchial, buccopharyngeal, cutaneous, or pulmonary.

The ability to breathe through skin, which is called cutaneous respiration, is a common trait in amphibians. Cutaneous respiration is also employed by all amphibians to various degrees, although to a greater extent in caudates than in anurans (1).

Adult lungless salamanders lack both lungs and gills, and rely on cutaneous respiration. Skin, in fact, is the primary respiratory surface in most amphibians and must be kept moist.

In anurans (a tailless amphibian of the order Anura ; a frog or toad), cutaneous respiration occurs primarily as a means of carbon dioxide exchange, with the majority of oxygen exchange occurring in the lungs. Most caudates, by comparison, take up most of their oxygen through cutaneous respiration, even in species that possess lungs. Respiratory capillaries are concentrated in the skin in taxa that rely on the cutaneous route as the primary site for gas exchange, as in the lungless Plethodontidae and aquatic Cryptobrachidae.

The cryptobranchids ( large salamander) also use modified skinfolds to increase surface area and vascularization to enhance respiratory exchange underwater.

Skin folds of salamander

Image source: Wikipedia

Their skin has to stay wet in order for them to absorb oxygen so they secrete mucus to keep their skin moist (If they get too dry, they cannot breathe and will die). Oxygen absorbed through their skin will enter blood vessels right at the skin surface that will circulate the oxygen to the rest of the body. Sometimes more than a quarter of the oxygen they use is absorbed directly through their skin.

Source : Animal encyclopedia for kids

The frog is a good example. Essentially, a frog's skin is thin, and it has a lot of blood vessels. Oxygen diffuses into the skin through those blood vessels. The vessels also allow carbon dioxide to escape.

It's similar to the process that happens inside our lungs.

Tadpoles have gills, which eventually go away, because adult frogs grow lungs, but cutaneous respiration is helpful in winter, when frogs often hibernate underwater. Frogs don't have to get their oxygen from the air. Frogs usually hibernate in oxygen-rich water, which is how they can breathe all winter long.

That slime, though, is a mucus coating, and it actually helps frogs with their cutaneous respiration. They can only breathe through their skin if the skin stays moist; otherwise, a frog couldn't get enough oxygen or get rid of enough carbon dioxide. (2)

Footnotes:

1. https://www.sciencedirect.com/topics/veterinary-science-and-veterin...

2. Frogs Can Breathe Through Their Skin