Free-range eggs:  These are eggs from hens that have access to a large outdoor area, although they may be fenced in to protect them from predators and thus not totally "free." 

Omega-3 eggs:  Research has shown that including about 10% flaxseed in laying hens' diet results in eggs with a high level of omega-3 fatty acids.  Omega-3 fatty acids are a desirable component of a heart-healthy diet.  Eggs labeled as high in omega-3 must be tested to verify their omega-3 composition.

Organic eggs are produced in compliance with the National Organic Program standards.

Pasture-raised eggs:  This is nearly the same as free-range eggs; it assumes that the hens have a large outdoor area.  Pasture-raised also means that the hens get a portion of their diet from grasses and other pasture plants.