The inscrutable protector of Sigil, the Lady of Pain is more or less a complete mystery. She appears without warning as a robed woman floating a few feet above the streets, her face surrounded by metallic blades. She is also referred to as simply the Lady or Her Serenity, in reference to her perpetually vacant expression. She never speaks, communicating her will only through her servants, the Dabus.
The Lady protects Sigil from threats to its safety by controlling all portals within it. This was most recently demonstrated in the Tempest of Doors in which, following the Faction War, she closed all of Sigil's portals, finally reopening them in a reorganized configuration. The Lady's power prevents any god or divine being from entering Sigil, holds off major threats to the city, including the Blood War, and also bars any from entering Sigil by any means except through portals.
In addition to her control over portals, the Lady of Pain can personally deal with those who offend her. Any who are touched by her shadow are flayed, dying in fountains of blood as their bodies sprout innumerable cuts. She can also banish challengers to her Mazes. Those who are mazed are trapped in an extradimensional prison, inescapable except, it is said, by one hidden portal meant to drive the prisoner mad with its inattainability.
The Lady's power is unknown. Since her authority in Sigil is apparently absolute and she seemingly bars even the gods from entering it, many conclude that she is more powerful than the gods, even going so far as to speculate that the Lady is the most powerful entity known.
Despite her tremendous power, the Lady apparently forbids any to regard her as a deity. Those who worship her, even unaware of this disapproval, are typically flayed.
Though some wildly speculate, no one knows exactly who or what the Lady of Pain is, where she comes from, what she is truly capable of, or even whether she is ruler or prisoner of Sigil.
Note: There is a common habit with players and DMs who are new to Planescape to object to the Lady's innate power, or ask how to 'kill her off'. In general, questions along those lines are scoffed at by older players. The Lady of Pain is intended as flavor text, not as a personality within Sigil. DMs are recommended to use her as background flavor, a setting mechanic, and ultimate mystery - and to use her sparingly at that. Attempting to kill off the Lady makes about as much sense as attempting to kill off the sun or the sky.
"Keep the Lady of Pain a Mystery"