Remember that this game is based on the same "Fabula Nova Crystallis Myth" myth as FFXIII. Bassically in this game we also have the same 3 gods, but then in a more human like apperance.
In this universe Arecia (Mother) is the servent of Pulse. In order to open Etro's Gate she creates the 4 crystals which basically act as the Fal'cie of FFXIII, in other words brands people as I'Cie to do her bidding.
We also have Gala who basically acts as Lindzei. He's more of an unseen guy only appearing right at the end of the game when he takes control of Cid.
In the opening of the game you also see Diva. According to the myth of Fabula Nova Crystallis she would be te creator of the world, but in this game she mainly acts as the narrrator.
Now story wise the world of Orience is stuck in a spiral to open Etro's gate. Every time when Tempus Finis arrives and the gate to Etro hasn't opened the world will reset itself and start all over again. You can do this yourself in the game when you choice to become a I'Cie after which you get dropped in a battle you literly can't win.
Only a selected few know of this endless cycle which basically comes down to the 3 gods and there direct servents. When we play the game the cycle has already been repeated over 6 hunderd million times.
Arecia's way to open Etro's gate is to collect pure souls who can surive tempus finis. There are 16 of these souls though over time she droped 4 from the experiment. From these 4 Tiz and Joker somewhat became her servents, the other 2 are actually Machina and Rem).
Diva on the other hand simply tries to create a flood of souls to brute force Etro's gate open. I don't know for sure, but I'm guessing he's the one who made Cid start the war to begin with.
That's the setup. However when we get to Temple Finis we can only finish the game by recjecting to become a I'Cie. Instead we choice to give up our own lives to defeat Gala. This means we've diverted from the normal spiral. Wanting to know why this happens Arecia actually goes towards the crystals of Machina en Rem (you can watch this in that extra cutscene). Having heard the story she then decides to not reset the spiral, but instead she awaken Machina and Rem and remove the crystals from the world.
Now why the rest of Class Zero manages to talk that long and still die at the end is also a mystery for me.
Believe this was the extra ending video:
https://www.youtube.com/watch?v=8hYmgIjkW3w