I'll just copy here the explanation from the Magius themselves:
Huge wall of text incoming
Touka: "Our goal, you see, is to free magical girls..."
"From the shackles of the witch transformation."
"I'm sure you know of this already?"
Yachiyo: "Yeah, we already know."
[now fade to white with just Touka]
Touka: "The foundations of this are already in place here in Kamihama."
"That meddlesome Kyubey isn't around, and you already can't become a witch, right?"
"Don't you think that's ideal?"
"Aside from having your soul gem crushed, there's noooothing to be afraid of anymore."
"And so what I want is to spread that over the entire world."
"While protecting and raising witches, and making lots of rumors."
[back to the field by the Ferris wheel]
Yachiyo: "You want to spread this area where you cannot become a witch across the entire world?"
Touka: "Precisely."
Yachiyo: "I understand what you want now, but that doesn't explain anything."
Tsuruno: "Yeah, by what logic does that require witches and rumors?"
Touka: "Come on, don't rush me!"
"Um, you see...'
[fade to gray]
Touka: *The reason that we use witches and rumors is because we want energy.*
[insert image of the Rumor of the Townspeople Horse]
Touka: *The energy that the people of Kamihama exhibit when they're happy or sad because of rumors...*
[insert image of the sheep witch]
Touka: *Or the energy that witches save up, or the energy from when a magical girl transforms into a witch...*
[insert image of ? squiggly]
Touka: *By using all of this saved up energy, we can release everyone."
[Alina shows up]
Alina: *That's how it is.*
- We are using all the gathered energy to promote the incubation of the Embryo Eve.*
Nemu: *And as a result, if all three Magius are together at the time of the hatching of the Embryo Eve, we can face the world from Kamihama here and cause a miracle to occur."
[back to the field]
Nemu: "If we are able to realize that, it will be an unparalleled victory, akin to winning a war of independence."
Touka: "Right!"
"Having become independent of the existence known as Kyubey, humanity will be acknowledged across space."
"If we can do that, it might take many thousands of years..."
"But humanity might be able to explore the entirety of the universe."
Nemu: "For me, it won't be just Kamihama."
"I'll turn the entire world into my manuscript and realize all kinds of stories."
Alina: "And I will have my artwork reign forever as a symbol of life."
"Next I will entrust my soul to art patterned on the universe."
Touka: "Of course, all the magical girls will be all happy happy for being saved."
Momoko: "Being acknowledged across space? That's quite a leap there..."
Rena: "And what is this Embryo Eve thing..."
"This is making my head hurt..."
Felicia: "......u-uhh."
Kaede: "And Felicia-chan has frozen..."
Yachiyo: "sigh..."
"I have all sorts of things I want to ask, but let me have this one question."
Touka: "Go ahead."
Yachiyo: "Why, with such lofty ideals, do you need to make use of humans?"
Touka: "Did I not say?"
"Isn't it better to use people who are worth less than magical girls first?"
"There's a risk involved in everything, so we have to use what we can."
Yachiyo: "So I just needed to ask this from the start..."
Iroha: "..."
Tsuruno: "Iroha-chan..."
Iroha: "Leaving aside my memories..."
"Even if you're the Touka-chan and Nemu-chan I liked..."
"It still isn't good to do..."
"No matter how long you spent thinking of this..."
"Even if you wanted to save everyone..."
"There are things you mustn't do..."
"Do you two think it would be okay to kill your families like this?"
Touka: "..."
"Hmf. Does everyone else think the same?"
[we see all of Iroha's allies]
Touka: "..."
"Well fine then, we didn't get anything out of explaining."