I don't know what the source of that synopsis is so I'm going to be working off of the official site and Wikipedia.
The term 先祖返り (senzogaeri) refers to a descendant who manifests traits of distant ancestors. I looked into it a bit more, and the formal term appears to be
atavism. Since atavism refers to the phenomenon and not the person, I assume that makes the person an atavist (yes, it's a real word, I looked it up).
In this series, "Atavist" specifically refers to distant descendants of Demons (
youkai) that mated with humans. An Atavist is someone who suddenly manifests Demon traits, even though for generations their parents have been normal humans.
Clans to whom an Atavist is born are rumored to prosper, and thus Atavists are hailed as the second coming of the clan's Demon ancestor. However, as you might expect, there are many who fear, hate, and seek to kill Atavists, since they hold such strange Demon powers. Our heroine Shirakiin Ririchiyo (CV: Hidaka Rina) is one such Atavist, the descendant of an
oni. Being an Atavist, she's constantly targeted, and so she's looking for a bit of security.
Now that the background is out of the way, on to the introduction from the website:
* I transliterated it straight from the Japanese, but I think the first two words are meant to represent something in another language; French perhaps. "Mansion du Ayakashi"? I don't know French, I'm afraid.