The One was an interstellar entity that built Vuffi Raa to explore the Galaxy and its civilizations. Together with an entity known only as The Other and an immense gathering of other entities known only as The Rest, The One was actually a droid manufactured by a starfish-like species who had gone extinct when the sun of their planet went nova. Their droids, however, "lived" on and eventually achieved full sentience.
Like others of his kin, The One was a tremendously powerful, starship-sized droid who was able to fly from one side of the galaxy to the next. His "son," Vuffi Raa, is presumably the first droid of his kind, as well as the first droid to be built by another droid of this extinct species instead of built by the species themselves.
After allowing Vuffi Raa to roam the Galaxy for many years, The One began searching for his offspring to bring him home. Together with The Other and The Rest, the massive droid followed a trail of clues that led them to the ThonBoka, where Vuffi Raa was helping his latest master, Lando Calrissian, to defend the native Oswaft against the wrath of the Galactic Empire and their Centrality allies. Threatening the Imperial/Centrality fleet with destruction, The One and his cohorts forced the Imperials and the Centrality to quietly leave.
Unfortunately, Vuffi Raa had been blasted by the evil Sorcerer of Tund Rokur Gepta when trying to defend Lando, though with The One's technological abilities, he was repaired to full capacity in no time. Once Lando bid his mechanical friend a tearful farewell, Vuffi Raa left with his mechanical kin to fulfill his destiny.