The origin of Psycho Twilight is in the episode "Lesson Zero" where Twilight Sparkle actually goes temporarily insane due to extreme pressures and stirs up trouble so she can help out. The dark tones of this episode coupled with her exaggerated facial expressions and crazed voice made some viewers latch onto the "Accidental Nightmare-Fuel" elements much as they had done in the past for other ponies going "insane".
Psycho Twilight is a common sight in YouTube parodies, usually showing the infamous scene in which she first appears to the Cutie Mark Crusaders appearing quite menacing despite the family/kids-friendly nature of the show.
Psycho Twilight is considered by some fans of "troll humor" as a sidekick of Molestia, another parody of Celestia and a meme in her own right.
The meme is infamous in part due to the fact the episode in which it originates actually does depict Twilight Sparkle in a negative role, so much so that she can be seen as the antagonist of that episode (albeit due to suffering what appears to be a mental breakdown).
In her desperation to "help" her friends she tries to deliberately cause trouble, going as far as ambushing the Cutie Mark Crusaders and trying to get them to fight amongst themselves so she could "help" them: her mental breakdown is often compared to the infamous Pinkamena incident in "Party of One" as well as Fluttershy's now iconic temper tantrum during the "You're going to love me!" scene arguably though Twilight Sparkle was the only one who actively became antagonistic.
The episode which inspired the "Psycho Twilight the Big Bad Pony" meme is remembered as being one of the darker and more memorable episodes in the series - though it is worth noting almost all of the "Mane Six" have had a similar mental breakdown, Twilight Sparkle's was just more pronounced than usual and quickly sparked the imagination of fans (as well as internet "trolls" (in this case "trolls" being those who use it more for comedy than malice).
In the canon story Twilight Sparkle actually does cause trouble and becomes a somewhat willing antagonist - desperate to "help" her friends she becomes insane when no one requires her aid and thus decides to make trouble so she can fix it.. she does this by enchanting one of her old dolls, yet the spell backfires and soon most of Ponyville is in chaos as they fight over the doll: ultimately Celestia intervenes and Twilight Sparkle's trickery is exposed, shaming the young unicorn as she learns a somewhat harsh lesson about misuse of magic, though like most episodes it ends happily and Twilight Sparkle (of course) redeems herself.
The original meme picked up on Twilight Sparkle's dark and unstable nature during the episodee, which paralleled Pinkie Pie's descent into madness during "Party of One" - thus the name "Psycho Twilight" became widespread and by far the most popular image used was (and remains) her crazed smile, often accompanied by "Hi Girls" or similar: though sometimes the famous "Gollum" scene is used instead, many fans also make use of the "twitchy ears": which they find amusing as well as slightly disturbing.
Another scene frequently found in "Psycho Twilight" memes is the "Clock is ticking Twilight, Clock is ticking!" - due to the crazed expressions she uses as well as a fan-theory that Celestia was deliberately taunting her with the erratic movement of the sun in the sky (see Trollestia).
Spin-Offs / Notable Mutations
- The episode "Lesson Zero" should have been banned due to Snapple's insane personality due to being a TV-Y-rated show.