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The air comes in contact with the moist respiratory surface of skin directly and of lungs and lining of buccopharyngeal cavity during the breathing process. The O2 of the air dissolves in the moisture and diffuse through the respiratory surface into the blood and the O2 from the blood diffuses through the same surface into the surrounding air. 
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Cutaneous respiration in frogs means the respiration,i.e., exchange of gases, is carried out through the skin of the frog.
The skin of frog is specially devised with numerous blood vessels so that it can absorb the oxygen from the surrounding water through a process known as diffusion.
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