My mother taught me this term when I was fairly small. I had an intuitive understanding of it, and I'm not sure I ever asked her for a definition. Still, you may need one, so here's an attempt...
There are times when you craaaaaave touch, a prickly and almost-but-not-quite-pleasurable burning. If someone brushes against you, you want to butt back like a cat. But it's not purely tactile; if it was, a hug from a friend would satisfy. Instead, the touch has to be suggestive, sensual or openly sexual, or the burn continues. Skin hungries is the mindless desire that leads to one extra cocktail at bar time and waking up next to the wrong person.
Guess what I have.
I kind of enjoy this torture. It makes me see and appreciate the beautiful bodies around me. It makes me bolder in casual situations - I'll hold a gaze longer, smile more slowly, play dangerously with language. I walk the knife edge with perverse enjoyment.
I am a hazard at the moment. You've been warned.