
Not really 10 year old explanation but hope it helps!!
What I got from her explanation, was an idea to change society in their world into something resembling what our current society is like in the real world.
So Monarchy (feudal system) like kings, nobles, knights, slaves etc. is what they have now. Except the whole weird thing the lords did by giving incentives to the woman to make them feel important / better from not having enough men to go around to get married to. The plan backfired! The woman took all the power and the men became slaves. They just left it like that thinking it would die down
╮( ̄▽ ̄)╭ and now they want get rid of anyone who is a weak link/showed their true colors. Like owning slaves, pushing their weight around etc.
What they want to do next is take down the Monarchy system. So everyone has equal rights. She mentioned a centralized system, so I guess introducing a government system. Not sure how they will go about it. They could either have someone become president/prime minister...maybe a few cabinet members under them (Will voting be a thing? ) Nobles that didn't participate in such practices, wanted to get a leg up on the completion. And have favoritism on them when it does change. So they will have a higher chance at getting a prime spot in the new government.

Oh and I forgot they introduced the academy and opened it to the commoners as a way to start changing their perspective. Make them more opened to the new ideals. And know they can have a voice in this new world. But it's been pretty lacking in those terms. I feel like MC will be the catalyst to all this change/have a high position.
Explain it like I'm 10 years old.