The terms "Free Range" and "Free Roaming" mean that hens have "been allowed access to the outside," according to the USDA. There are some third-party verification programs, too. "Free Range" usually means the laying hens are raised in large flocks in big open warehouses rather than in stacked cages. They can walk around, flap their wings and preen their feathers. But outdoor access is not clearly defined - it is probably very limited, and on dirt or concrete rather than pasture. "Cage Free" does not mean outdoor access.
"Certified Humane."
Humane Farm Animal Care operates a certification program specifying that laying hens are uncaged, with access to perches, nest boxes and dust bathing areas. There are stocking-density maximums, but outdoor access is not required. Beak trimming (but not debeaking) is allowed; starvation to induce molting is prohibited.
"Certified Organic."
Production methods must comply with the USDA National Organic Program, including organic, vegetarian feed, no use of antibiotics and no cages. Debeaking and forced molting by starvation are allowed. Organic standards require producers to "maintain livestock living conditions which accommodate the health and natural behavior of the animals." How much access to the outdoors this requires for chickens is still being debated. On large organic chicken farms, it may mean nothing more than a small door opening onto a concrete yard.
"Omega 3."
All eggs contain small amounts of omega-3 fatty acids, thought to be beneficial to human health. Omega-3 levels in eggs can be raised by supplementing the birds' diet with fish oil, flax seed or alfalfa meal (or by simply allowing the birds to forage on lawn or pasture).