The Other
The "Other One" is only mentioned once in the series, in the episode The Why of Fry. This takes place as Fry is to decide whether he should let history take its course or get his life in the 20th century back, under the desk at Applied Cryogenics on December 31st, 1999. When Nibbler asks Fry if there is nothing in the future that he wants, Fry answers that it is Leela. Nibbler then says that she may be the "Other One" and that Fry cannot give up on her, and that he will give Fry assistance in the matter.
The significance of the "Other One" is one of the major mysteries and cliffhangers in the series, caused by its untimely demise - the storyline involving Fry, the Nibblonians and their conflict with the infernal Brain Spawn was cut short before it could be elaborated some more. There are various theories about the "Other One". Some claim that Leela may have as much significance for the struggle against the Brain Spawn as Fry does, for reasons yet unknown. Some go as far to say that Fry can only defeat the Brain Spawn for good with the help of Leela. Others say that Leela may play the role of a guardian for Fry, protecting him from danger so he can fulfill his task - this seems logical, as Fry is frequently saved from harm by her. There is one more possible explination: since Fry told Nibbler in 2000 about Leela, he could remember that for The Day the Earth Stood Stupid, then help Fry.
At the moment, we are left with speculations. One of the movies may point this out or explain what it means...