Onionskin is a very thin, nearly see-through paper, and the poem builds its whole feeling from that fragility. The speaker says "we are worn so clear," and the "we" seems to be the papers themselves, or perhaps people who feel as thin and see-through as they are. Being worn clear suggests being rubbed down by time or use until almost nothing is left to hide.
The second part makes the mood darker. The papers are "impossible" and "fasting / alone with a match." Fasting gives them a quiet, self-denying patience, as if they are emptying themselves out. The match is the threat, and maybe also a kind of release. Paper and fire sit side by side with no one around to stop what might happen.
The speaker doesn't say whether this is sad or freeing, and that ambiguity is what stays with you. The poem feels hushed, brittle and strangely calm, like waiting at the edge of disappearing.