Ok, let me try giving you my explanation.
In this universe, demons and humnas co-exist. Demons & humans each have their own areas.
There exist, I would almost call them legendary demons. Demons with power far beyond that of any normal creature, in a sense most of them are witches and vampires.
The story is centered around Akatsuki Kojou who "received" his powers from one of these legendary vampires, making him known as the Fourth Progenitor.
Now basically there are different "police" type organisations who keep a watch over these area's/worlds, one is called the Lion King organisation (stupid name

).
They send a young lady who wields one of the most powerful "divine/holy" weapons to observe this Progenitor and to make sure that he can be dealt with if need be.
Trouble, turmoil, destruction, fighting, various love interest and funny characters follow the series.
Its a really cool series, which I'm really looking forward to watching each week