Black Lady was the form Chibiusa took when she was turned to evil by Wiseman.
In the anime, Chibiusa travelled to the future with the Sailor Senshi and once there, heard King Endymion tell them that the Silver Crystal disappeared shortly before the Black Moon Clan attacked.
Thinking that it was her fault that the Crystal vanished, and thus her mother was hurt, she became upset and ran away, leaving the shield around the Crystal Palace. Wiseman found her there and began showing her illusions that made her think that everyone blamed her for what happened. He told her that he could convince everyone that it was not her fault, and by taking advantage of her emotional weakness, used his power to transform her into Black Lady.
The first time Sailor Moon encountered Black Lady, she tried to use the Silver Crystal to turn her back; it almost worked, but Wiseman appeared in time and persuaded her that her memories were not real and her friends and family did not really care about her. When Sailor Moon tried again later, Black Lady deflected the Silver Crystal's power and was unaffected by it.
In their final battle, Black Lady attacked Sailor Moon, but Tuxedo Mask protected her and took the blast. Black Lady was stunned by this selfless act, and the Senshi tried to convince her of their love for her. Wiseman attacked in an attempt to stop them, but Sailor Moon managed to use the power of the Silver Crystal to transform into Neo-Queen Serenity, her future self.
Sailor Moon and Tuxedo Mask together overcame Wiseman's power and convinced Black Lady to transform back to Chibiusa.
In the manga, Chibiusa accidentally dropped her Time Key and wandered into the Fourth Dimension. When she became lost and scared, she decided to return but found she no longer had her Key. Wiseman confronted her and lured her to him preying on her loneliness. She took on her new form as Black Lady and gave the future Silver Crystal to Wiseman - though he was unable to use it. Mamoru had followed Chibiusa into the storm in the Fourth Dimension and he became trapped in the spell of the Black Moon as well.
It was Black Lady that called forth the true form of Wiseman, the planet Nemesis, then commanded Mamoru, now under the power of the Dark Moon, to take Sailor Moon's brooch and Silver Crystal of the 20th century. Prince Dimande took the crystals from Black Lady and planned to touch them together, resulting in the destruction of everything. However, Sailor Pluto used her forbidden power Time Stop to keep the crystals from coming in contact. Because this was taboo, she died. Seeing Pluto die caused Black Lady to remember who she truly was and awakened her powers as a Sailor Senshi, Sailor Chibi Moon.
In the musicals, Black Lady was played by Mao Kawasaki, who formerly played Chibiusa, and Shion Nakamaru. Her image song was "Black Moon Signal," and she shared a duet with Chibiusa, "Kono Kodou Kara Yoru wa Umarenai."
Last scene when Black Lady appears
Black Lady "attacking" Sailor Senshi