If you work to iron a stubborn wrinkle out of your shirt, you're trying to smooth out a crease. A wrinkle is a dent or line where that smoothness is interrupted.
You might fret about a wrinkle in your skirt or a new wrinkle on your face. Another kind of wrinkle is more figurative: a small complication or problem that arises suddenly. You could describe a torrential rain storm as a wrinkle in your plan to film a sunny scene in your movie, for example. The Old English root is gewrinclod, "wrinkled, crooked, or winding," and it comes from the verb wrinclian, "to wind."