Organic eggs are required to be "cage-free" though that doesn't mean they're running around in pasture. Cage free means just that, not in a cage. They are able to be kept in barns with small doors that periodically offer a chance to go outside the barn to an enclosed area. Better than cages, but not free-range, pastured chickens or anything.

Ultimately, not much means much insofar as definitions for eggs. Read this from the USDA (page 6):
http://www.ers.usda.gov/Publications/LDP/2006/12Dec/LDPM15001/ldpm15001.pdf

Note especially all of the things that eggs or chicken are labeled that "don't require third party certification."