Grandmother is the name of... something. Some believe 'her' to be God's evil twin, others think 'she' is the remnant of a dead universe, and still others point to 'her' as Oblivion itself. What 'she' is exactly is never known, but what is known is that she is ancient and wants to consume every living soul on earth. Grandmother is the major driving force behind many of the events of Orpheus, particularly the last two books in the series. Her common name is derived from the term "the Grand Maw" which sounds close to the term "Grandma". Hence, she became known as Grandmother.
She is also known as the Infinite Maw and the All-Devourer, and is the "mother" of the Malfeans. Like her offspring, she slept beneath the Underworld until awakened by the Sixth Great Maelstrom. She revived with a great hunger, and her children now seek to stop her from consuming the world lest she consume them as well. She constantly chews through the ever-shrinking Labyrinth, seeking to consume the Tempest, the Shadowlands, and, eventually, the world of the living. She controls armies upon armies of Spectres, which she uses to fight the Malfeans. As she is also tied into the hive-mind, she keeps many of her darkest, most important secrets in Memory Towers.
Ironically, Grandmother herself is significantly less malevolent than her minions; she honestly does not comprehend beings outside of herself have wills of their own and may resent being devoured. At her core, she is a creator rather than a destroyer; her motive, as revealed in End Game, is to remove the "psychoses" that are the rebel Spectres, and devour enough energy to make her own universe. Sadly, this would mean "everything on Earth."