Cage-free, on eggs, means the hens were not kept in the small battery cages that hold birds almost still. They can walk around. That is all the label promises. Though actually it does not mean they went outside — that is free-range — and it does not mean organic, and it does not by itself mean a gentle farm. Cage-free hens are often packed into large indoor barns. The word comes out of animal-welfare argument and then stuck on cartons; you will sometimes hear it about other farmed animals, but eggs are where students meet it. It is marketing-and-shopping English, mildly official-sounding, not poetic.