means A small crease or fold in skin, fabric, or any surface — or, figuratively, a clever new twist or a snag that complicates things.

from From Old English, where a verb roughly meaning 'to wind' or 'turn' gave rise to gewrinclod, 'crooked, winding.' It belongs to the same family of words about twisting and bending that gives us 'wrench' and 'wriggle' — anything that won't lie flat. The 'new wrinkle' sense (a fresh idea or angle) is much later, an English play on the idea that a wrinkle is an unexpected fold in an otherwise smooth plan.