In the continuity of the live action film, Alita: Battle Angel, The Fall refers to the Great War between the Imperium and the United Republic of Mars, its aftermath, and the beginning of the Dark Age that followed. The War began in the 23rd Century A.D. between the Earth-led Colonial Empire and the United Republic of Mars, and resulted in the death of most life on Mars along with the loss of colonies and cutting off of Earth from space Travel, along with human civilization becoming consolidated heavily in Iron City, which in turn survived on a symbiotic relationship with Zalem above.
With the dark age that followed, most of the details about the Great War are left unknown, except tahat Zalem (Tiphares) survived as the sole floating city on Earth, along with the destruction of the colonial empire, isolation of Earth from space, and Alita being left as an apparent sole survivor of the war, aside from Desty Nova. Some time before the turn of the 23rd Century, Mars and other related colonies had become independent of Earth and The Imperium, as the URM, or United Republic of Mars. Hostilities arose, leading to warfare occurring at various points, such as on Earth's Moon, as shown in Alita's flashback, eventually leading to a devastation of the two capitals, with an unknown virus being deployed by the URM on Earth and reverse-terraforming nanites being released on Mars. The virus was more than 70 percent fatal and highly contagious, resulting in a massive emergency quarantine being enacted by the various floating cities on Earth. Numerous attempts at fleeing to Earth from offworld colonies of the Imperium were made, many of which failed.
Mars was struck by reverse-terraforming nanites along with high energy projectiles. This attack left most life on Mars extinct, and the planet almost completely uninhabitable. Seeing their own people dying and facing apparent extinction, the URM consolidated its forces for a final desperate assault with URM Berserkers on Earth and it's floating cities. Alita and Gelda were both participants in the attempted strike on Zalem itself. Alita's body was mysteriously left in the scrapyard, buried in a state of hibernation, for over 300 years before Dyson Ido discovered her head and torso.
The effects of the Fall were devastating. Earth and Mars both were ultimately isolated and rendered mostly uninhabitable as a result of the biological and nanite superweapons utilized by the warring factions. The virus deployed on Earth by the URM was over 70 percent fatal, with others shown being crippled or scarred by its effects. Extensive quarantines were performed by the sky cities to prevent the deadly disease from coming into them. The quarantines remained largely in effect for over 300 years in terms of very few humans from the surface ever seeing Zalem, and none recorded as returning. 
Mars suffered a mass extinction from the reverse-terraforming, the planet was rendered mostly uninhabitable except for possibly special equipment such as space suits, although with the extensive isolation, and reports from Zalem or the space elevator being isolated from the surface, details are mostly unknown as to the situation on Mars following the destructive nanite attack. Alita's birth parents on Mars are presumed dead due to the long time from the Fall as well as the brutality of the attacks.