means the typically flat, green outgrowth from the stem of a plant that captures sunlight for photosynthesis — or, by extension, a single sheet of paper in a book.

from From Old English 'leaf,' with cousins all across the Germanic family — Dutch 'loof,' German 'Laub' — and a deeper root that likely meant something stripped or peeled off. The 'page of a book' sense is no metaphor stretch but an old, intuitive leap: a book unfolds in thin sheets the way a plant unfurls its foliage, which is also why we 'leaf through' pages and why a folding table has a 'leaf.'