What is the trait that distinguishes primates, rodents / rabbits, crocodiles, and dinosaurs / birds from amphibians and earlier lineages?

The first land animals had to adapt to this whole new set of conditions that were significantly different than the ones in the water.

One of the biggest challenges was to protect the embryo in these new harsh conditions. The amphibians and members of earlier lineages such as fish are dependent on water for their reproduction, but reptiles, birds, and mammals have developed the amniotic egg during the course of their evolutionary history enabling them to produce offspringing on the ground.

Members of this group either carry their offspring inside the female's womb or lay eggs that are protected with an outer tough layer. Both the young in the womb and the ones inside an egg are protected but the embryonic membranes amnion and chorion that contain water and nutrients necessary for the development of the embryo and therefore are called amniotes.