I think I watched all the anime episodes and I still have no idea how their powers/universe works. I probably stopped trying to get it when a naive teenage girl became a god.
The issue goes like this (SPOILER ALERT):
They all are, first, ordinary girls. Their powers come from a pact with Kyubey, which is able to guarantee any desire in exange for the "crystallization of their souls" (the creation of the Soul Gem), since in this process Kyubey is able to get some kind of "energy".
The problem with this agreement is that it has trap: crystallize the soul (and use it to generate the "magic"), makes it contaminated. To clean it, magical girls are forced to defeat the "Witches" to get the Greed Seeds, because otherwise they are victim of all kinds of negative emotions (despair, jealousy, agony, etc.), which lead them to finally become Witches.
The existence of witches, ironically, gives a reason to Kyubey to try to create more Magical Girls to combat them, thus achieving a technically infinite energy cycle. Obviously, they care nothing about the cruel cycle he throw the girls who he seduces to become Magical Girls. His only worry is collecting their share of energy.
Technically this will be an endless cycle... except by the power of Homura. Since her wish was "to return to meet Madoka" she has the ability not only to stop the time in the present moment, but "reset it" (something like jumping from one timeline to another not "spoiled"), something which she makes again and again in their efforts to avoid Madoka falling into that circle (trying to avoid she become a magical girl).
With each restart, however, the magical potential of Madoka increases. With each "new beginning", the energy that Kyubey can get from Madoka if she becomes a magical girl increases. The stakes rise and rise with each new desperate Homura attempt, until the whole truth is revealed and Madoka take a decision: break the vicious circle betwen Magical Girls and Witches creating a new one, The Law of Cycle, which dictates that witches don't exist, and when a magical girl falls into despair, her soul is saved and preserved for eternity (preventing thus the existence of the witches and screwing the snack bar of Kyubey).
Achieving this would be, according Kyubey, impossible because you would need the power of a God to get it, which is precisely what Madoka has accumulated through endless repetitions caused by Homura.
As a result, by asking her desire (Save ALL the Magical Girls), she becomes a goddess and her existence, as well as the awareness of the existence of witches, is eliminated from the world (so only Homura remembers her for yuri reasons xD) to shape this new cycle Salvation.
So far the anime / the first two films.
The third film reveals that despite not even remember Madoka or "knows" the existence of witches, Kyubey find interesting that possibility and its "energy potential".
So he decides to do an experiment, and when Homura is about to die (and therefore her soul be "rescued" by the Law of Cycle) Kyubey isolates her, confining in a place where nothing and no one can, allegedly, reach she, just to see "what happens."
Given this confinement, Homura becomes inevitably a witch. And, like any other, creates a labyrinth (in this case, the false Mikatahama city) in an unconscious desire to recover all she lost. As a result, to the labyrinth are "invited" several presences which Kyubey opens access to see what happens, because among them is the "mythical" Madoka.
In this hypothetically "perfect" life in which finally they are all alive and all live in peace, is ironically the "aware" conscious of Homura which perceives that there is something "wrong" (Madoka can not "fiscally exist"! They fought witches (first) and spectra (after), not nightmares!) and discover that ALL is a work of a witch. Shortly after, she also realize that she is the witch in question.
Desperately, she surrender to the despair and full transform into a witch, with the hope that the rest of the magical girls will defeat she and become free from their own trap. Meanwhile, with the help of Miki and Bebe, the plan of Madoka (deprived of her divine powers and memories while she is inside the confinement) is break the isolation imposed by Kyubey from inside to be able to reach Homura and "save" her.
For better or worse, Homura has other plans. She isn't willing to "lose again" Madoka being carried away to the Law of the Cycle. So, when Madoka finally reach Homura, she literally steals her divine powers, transforms herself into a Goddess (she calls herself a "demon") and changes again the law, creating a new reality in which, once again, all are alive and don't remember what happened. Her only obsession is to be with Madoka, even if keeping she "sealed" is needed.
Unfortunately the third movie ends here and it is uncertain if they will continue with the franchise or not, but there are plenty of doujins toying with the idea of what could happen with this new world and all its protagonists.
I don't know if I will have clarified something to you, but I hope so. ^^"
PS: All those black bars are an insufferable sight. xD
If you consider that the above is perfectly reasonable and don't need them, I will remove them gladly.
last edited at Apr 6, 2016 8:04PM