I've noticed this mask being used by almost every major antagonist in the anime. It's mostly used by them as some sort of a gateway to call the Phantoms (Ayakashi) but what exactly is it?
The masks are a medium that utilises the power of Hell to call forth Ayakashi and they basically materialise Izanami's power in our world. The masks are created by Fujisaki Kouto, Yato's father. The are created using the power of the Yomi no Kotonoha (Words of Hell), which are used through paint brushes that utilise the power of Izanami. He currently possesses two brushes, his own and Ebisu's. The ability the brushes provide are of course masks summoning and the control over Ayakashi.
Masks Summoning: An ability she obtains from using the Mandate of Hell (Phantom Brush). She is able to summon phantoms without chanting or affixing a mask, and without sustaining blight in the process, unlike Ebisu.