sauceBuniberuze (?) is a god that controls everything in the world. He defeated his mother goddess Muin (?) and obtained position of god. Muin faded out to "invisible world". Buniberuze was suffering from pain because everything in the world had ending and nothing was eternal. Every life has to die someday. He was seeking for eternity. He thought the reason why everything has ending is because of Muin's curse. So he decided to find his mother Muin and kill her. He made three fal'Cie's.
The first fal'Cie was called fal'Cie-Pulse(it seems Pulse itself in FF13 was a big fal'Cie) and it was made in order to find the gate to reach "invisible world" . The second fal'Cie was called Etro(?) but Buniberuze made a mistake and Etro looked similar to Muin. He feared Etro so he did not give any power or roles to Etro. The third fal'Cie was called Linze (?) and it was made in order to protect Buniberuze and tell him to wake up when the focus is done. (I think Linze is cocoon)
Pulse made fal'Cie and l'Cie in order to expand the world. Linze made fal'Cie and l'Cie in order to protect the world. However Etro could not make anything. Etro felt lonely, so she bleed herself and faded. From the blood of Etro, human was born. Etro finally met Muin and Muin told her to maintain the balance of the world. After that, Muin faded to chaos completely and vanished. Etro could not understand what Muin meant. But she liked human and she gave them "heart"
"Heart" was "invisible world" that human carried. Time has past and human began to consider Pulse as a utility ruling god of the world, Linze as a guardian god of the world, and Etro as a God of death.
It seems like XIII's backstory which'll tie in together with Versus and XIII-2. In the new trailer, Lightning does mutter the word Etro, so there is some sort of connection. There's no clue as to whether this is all that'll be in the 'anime' or if it'll be broadened into a full OVA, but one thing is for certain in that SE is trying to make some sense of this compilation for us.