Nightmare Moon is Luna's alter-ego that she had taken form of 1,000 years prior to the series. It was this change that made Celestia banish her to the moon for the next thousand years, before she made her return, only to be defeated by the Mane Six once again. In an Alternate timeline, Nightmare Moon is the current ruler of the Lunar Empire.
Nightmare Moon is a tall pony, the same size as Celestia and shared many similarities towards her as well. Her fur color is pitch black, and her mane and tail flow in a starry midnight complexation. Nightmare Moon wears light blue armor with a moon emblem on her chest, and a helmet on her head. Her eyes are more reptilian-like, with her irises slit.
She is shown to be very forceful and angered towards her sister, as she is the manifestation of Luna's own doubt and jealousy towards her.
In an alternate timeline however, while she had shown a sort of force in her subject, she still has shown some bit of regret for her sister, and willing to listen to her subjects if they do indeed have something important to say. It's possible that Sombra's involvement made her more open-minded than she would normally be.
As an alicorn, is it possible that she has a very high level of magic, able to move the moon with ease, much like Luna.
Nightmare Moon came to life 1,000 years ago thanks to Luna's jealousy over her sister. She fought Celestia head on, but was end up banished to the moon. A thousand years later, she ended up returning, but after a while she too ended up defeated, this time by the Mane Six, and thought removed from Luna's body.
Nightmare Moon reappeared again after a curse from Sombra was placed on Luna for her to come out again as a distraction for Celestia. Nightmare Moon fought Celestia once again, but before the fight could finish, she was found by Tirek, and drained of her magic, making her inactive once more.
In an alternate world, Nightmare Moon is the current leader of the Lunar Empire. In her own words, Nightmare Moon returned far later, and confronted Sombra upon his return alongside her sister, just to watch her sister get killed. Nightmare Moon then waged war against him, worried that the advancing winter he brought with him will destroy Equus.
Twilight Sparkle and Spike went to her castle, and it began to peak her interest when she mentioned time travel. Nightmare made it clear that no creature more powerful than her is to live in her kingdom, as it could be a subject used against her. After some explaining, Nightmare explained to Twilight the current situation. Twilight promised her she'll make things right, to which Nightmare only hoped so.