While "pastured" can be used to describe any animal raised for meat or eggs, "pastured" is most often used to describe poultry and eggs from chickens who have been raised the way you might imagine a chicken would want to live: they walk around in open fields and woods, they forage for food (primarily seeds and insects, with the occasional small rodent or reptile if they can get them), and they go back into a hen house at night to roost, nest, and lay eggs.
Pastured animals often receive supplemental feed in the winter or during dry months. This feed may or may not be certified organic. Since they aren't crowded together in unhealthy conditions, pastured animals don't tend to receive unnecessary antibiotics or hormones.
Importantly, "pastured" doesn't have a legal meaning or certification process. Pastured animals tend to be raised on small farms and the farmers often sell at farmers markets and other direct-to-consumer methods. It is usually easy to find out more about a specific farm that sells pastured meat or eggs since they are often rightfully proud of how they care for their animals.