Certified Organic:

This means the hens have been fed an all-vegetarian, chemical free diet.  No pesticides, fungicides, herbicides or commercial fertilizers can be involved in any stage of the process.  They live uncaged, and must be allowed outdoor access, but the specifics of outdoor time are not regulated.  Third party verification is used to check compliance.

Certified Human:

This means that the eggs are from uncaged bireds, but there are no requirements for outdoor time.  They must be allowed to engage in natural behaviors, and the density of population is regulated.  Third party verification is required.

Free Range or Free Roaming:

This would be a wonderful label if there was actually any check for compliance.  It should mean that the birds are either raised outdoors or have daily access as needed/desired.  However, as there is next to no regulation, this label ends up meaning very little.

Cage-Free:

This means the birds are not kept in cages.  However, it does not require anything beyond that, and is neither regulated nor third party certified.

Vegetarian-Fed:

This indicates a more natural feed given, but says nothing else about conditions for the birds.