The origin of the prophecy began 10 years ago prior to the events of Persona 3. The Kirijo Group initiated research on Shadows, studying their true nature in hopes of finding a way to utilize their power. Through their experiment, the lead scientists came to know about the Fall. The Fall is destined to be the End of the World, where Nyx will descend upon the world, destroying humanity.
Later, the scientists came to know about the herald of Nyx, Death. Embracing death as a deliverance, the scientists began a massive project to gather the Shadows, hoping to resurrect Death, and subsequently, summoning Nyx. In the last stages of the experiment, however, Eiichiro Takeba, one of the lead scientists voiced out his silent rejection of the belief and interrupted the experiment. As a result, Death was forcefully separated into twelve parts. The remaining Shadows along with Death would later go berserk, destroying the facilities and created the phenomena of the Dark Hour and Tartarus.
Death was eventually sealed within a young child, and due to it being unable to reunite with his counterparts, the Fall was delayed for some time. When the protagonist arrives to the very first place the Shadow was created, Tatsumi Port Island, the Shadows became active again, along with the prophecy of the Fall.
Cult of Nyx
Near the end of the game, during January, a cult devoted to Nyx begins to slowly manifest throughout Tatsumi Port Island. This drastically alters the entire city; graffiti and posters begin to show up everywhere, and the number of people with Apathy Syndrome increases. People affiliated with the cult also will attempt to persuade the protagonist into joining and ushering in their beloved 'Nyx.'
Around the middle of January, Junpei Iori will invite the protagonist out to Hagakure, saying that it's Akihiko's treat due to a little bet they had at Yakushima. When they arrive, Aigis will pull out a newspaper with the flap opened to the section on the new cult, which also contains a picture of the cult's high priest, who is quickly identified as Strega leader Takaya Sakaki. In the interview, Takaya claims that the world is in a state of turmoil, and that there is little chance for hope. He then claims that a magnificent being is the only salvation for humanity, which is identified as Nyx. Takaya then states that he has received a blessing from Nyx, and has learned of her divine power. He further manipulates the public by stating that there are also 'those who have been blessed by Nyx' that use this 'blessing' for their own selfish goals. The group deduces that Takaya is attempting to make the public hate SEES by stating that they are, in fact, the ones responsible for everything.
This is made even more extreme if the player talks to a male cultist in the strip mall. He will state that Nyx will deliver the virtuous and save the believers. He then adds poison to his words by saying that the members of SEES will suffer by Nyx's divine guidance.
During the Fall on January 31, a group of cultists can be seen looking at the falling 'moon' as they fanatically embrace the coming end of the world. One of them, a beanie wearing man, begins to laugh maniacally before he becomes a Shadow and dies. Eventually, after Jin and Takaya were killed and the protagonist seals Nyx away, the Fall is halted, and the cult was presumably disbanded.
Persona 3 Club Book
In the Q & A section the Fall is revealed to be the rejoining of both Nyx pieces (the Moon and her psyche) which would result in the Moon crashing to the Earth to reclaim the pieces of her psyche (shadows) from the seal within Earth's creatures making her whole again.