Two short lines turn an ordinary idea upside down. We normally think of skin as something we have, a covering we carry around. Here the speaker says the opposite: skin wears the person, like a coat that holds them inside it. That reversal suggests a loss of control, as if the body is in charge and the self is just along for the ride.
The second line gives that body a restless life of its own. It "grows taut and it grows thin," which could point to tension, stretching, ageing, or fragility. The poem doesn't say which, and that openness is part of its effect. The speaker sounds quietly unsettled, watching their own surface change without being able to steer it.
The mood is uneasy but calm. The matching rhythm and the rhyme of "skin" and "thin" make the lines feel neat and inevitable, which only makes the idea of being powerless more chilling.