Lilith's Mirror is a mirror that has the ability to revert monsters to their true forms owned by the Tsukumogami, Lilith, which a Tsukumogami is literally a Japanese Yōkai monster known as a miniature fairy, sprite, or fae/fay (but "fay" is literally just another word for "fairy"), or even pixie.
In the anime, Kokoa wanted to use it to be with "Inner Moka". The plan, however, failed due to Tsukune's cousin, Kyōko running into Kokoa and taking the mirror (instead of the rice cakes) by mistake. After Kyōko finds out about the mix-up the Lilith of the mirror calls her master and Kyōko accidentally wishes that the students would reveal themselves. After getting attacked by many of the monsters, Kyōko and Moka team up and help restore the school to normal with Mizore, Kurumu, Yukari, and Ruby.
In the final chapters of the Season I, Ishigami reveals that she gave the Lilith's Mirror to Kyōko with the intention of stealing Tsukune's soul with an added bonus of releasing all of the students into their monster state through the powers of the artifact in order to create an uproar that would destroy the school. Lilith is later seen in chapters of Season II, seeing that she hangs around the Headmaster and Ruby, it is safe to assume Lilith has become good since her first appearance.