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, the Lich was never released, and there was no nuclear fallout to have created the Land of Ooo.
History
All of the standard timeline's events prior to the Mushroom War occurred, as signified by the existence of pre-War objects like the Enchiridion, and 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 mutagenic bomb, containing a green substance 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 mid-flight, 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 presently exist in this world. The ice crown remained dormant from not being used, and Marceline chose to stay underground to protect the crown and undetonated bomb, never becoming a vampire which would have stopped her aging process as it did in the original timeline. Some of the residents of Ooo would still exist but have remained as humans, like Choose Bruce and Bobby, who in the original timeline exist as Choose Goose and Billy due to the mutation of his ancestors.
Trivia
- The humans in the Farmworld look different than those seen in the standard timeline. They have more detailed eyes (white circles with black pupils) rather than just black dots and visible noses. However in Adventure Time Mini-Series: "Islands" some of the humans were seen with visible noses but all seem to have black dot eyes. Some say the reason for the eye difference is because the farmworld humans are "unmutated."