The Amniota also includes the dinosaurs, turtles, and lizards. Most of the early mammals were egg layers, the monotremes still are thus they (and we) are also included in the Amniota.

The egg of the Amniota is special. Working out from the embryo, the egg of the Amniota is a series of fluid filled sacks. The first layer around the embryo is the amnion, filled with amniotic fluid, which protects the embryo. The next layer is the chorion, which contains the amnion, the allantois, and the yolk sac. The allantois allows oxygen to reach the embryo and removes waste products from the embryo. The yolk sac provides food for the embryo and shrinks as the embryo develops.

Around the chorion is the albumin, the white of the egg, and lastly the shell of the egg, which protects it.

The placenta of the mammals is a modified egg, the embryo is still surrounded by an amnion filled with amniotic fluid. The allantois and yolk sac and part of the chorion have become the umbilical cord. The chorion has become the outer wall of the placenta, and connects the embryo to the uterine wall of its mother. It is the fluid-filled chorion, which "breaks" as labor begins.

Added with thanks to melknia:

Who points out that it was the amniote egg which allowed these animals to get away from water, which was a BIG evolutionary step.