Farmworld is an alternate timeline created when Finn wished that "the Lich never even ever existed" in the episode "Finn the Human." For this to have happened, the mushroom bomb would have had to not go off. In the alternate timeline created by this wish, Simon Petrikov froze the bomb. The bomb crushed Simon, killing him.
Therefore, humans did not become nearly extinct, and there was no nuclear fallout to have created the Ooo. Supposedly all of the residents of Ooo would still exist but would have remained as humans, like Choose Bruce who in the original timeline exists as Choose Goose due to the mutation of his ancestors.
It is suggested that in this timeline Finn becomes the Ice King rather than Simon Petrikov.
History
Similar to the history of Ooo, all early events prior to the Mushroom War occurred, including events known to have happened to the two known survivors of the war: Simon Petrikov (who would become the Ice King in Ooo's timeline) and Marceline. However, during the Mushroom War, a major deviation occurred that changed history.
During an attack where a massive bomb, possessing massive energy tied with the Lich is dropped upon Earth, Petrikov used the power from his ice crown to create a vortex that catches the bomb and freezes it, crushing him in the process. With his death, the ice power within him raged at the loss of its owner, and froze Earth into a pseudo-cryogenic state for 400 years.
Humanity remained the dominant species of the world and various environments continued to exist, including farms and arid areas. Some 600 years after the new Ice Age destroyed civilization, humanity has returned to a more or less medieval level of technology. The human race had achieved some technological advancement, such as the development of prosthetic limbs that can be used as weaponry.
Magic is known as to not exist in this world and the ice crown remained dormant from not being used. Likewise, Marceline chose to stay underground to protect the crown and undetonated bomb, and never became a vampire which would have stopped her aging process as it did in the original timeline.