According to Japanese mythology, Izanami, along with her brother Izanagi, is one half of the pair of sibling deities who created Japan.
According to legend, Izanami's brother dipped a jeweled spear into the sea, and the water which dripped from the spear's tip crystallized forming the Japanese islands.
Major Story Arcs
Izanami is the being that controls the Realm of the Windowless Rooms and as such a competitor with Lucifer (or whoever else is in control of Hell) as both realms desire more souls to fill them.
In order to remain strong in a world where the worship of gods is in decline, Izanami has been collecting many rare and mystical items that mortals think about, such as Rama's wedding gown, Lucifers Wings, organs of dismembered gods.
Lucifer discovers during a visit to her realm that she is channeling living dreamers into her realm, letting them pass through the many incarcerated souls, bringing misery to both. A discovery Lucifer would use to threaten Izanami into giving him his wings back or risk him summoning Dream of the Endless, who would be gravely offended by her poaching of dreamers. Izanami relents and returns the wings, though she plants a few extra feathers in it and swears revenge for the death of her sons.
In the DC/Vertigo version, Izanami appears primarily as a basalt statue of a naked and obese woman with thorns for hair. While Lucifer is in her presence, she doesn't speak, something she hardly ever does according to her son, and communicates through short hand gestures, leaving her mind and will to be spoken through Susano-O, who appears to understand her will better than most.