What Is Obliviasis
Obliviasis is an amnesia-like disease that has been spreading across the Planes since the Sundering. It causes progressive memory loss in those it affects. The disease appeared after the death of Darsea, the 10th Sovereign who governed the paired Aspects of Memory and Oblivion. The only first-party English text that names the condition, the official character profile of the researcher Otto, spells it obliviasis in lower case as a common noun; the Chinese profile calls it 遗落症. Community transcriptions of the beta have spelled the condition Oblivios or Obliviosis; this wiki uses the official spelling.
Origin
Kumyo Kyo is reported to have named the World-Ender as Darsea's killer, though how she died has not otherwise been confirmed. As the Sovereign whose authority encompassed Memory itself, her death had consequences that went beyond a single loss of life. With no one governing Memory and Oblivion, the Aspect destabilized. Obliviasis began spreading like a plague across the fragmented Planes, erasing the memories of those it touched.

The disease can be read as a metaphor for the game's broader themes: the Old World is being forgotten, the connections between things (the Nexus) are broken, and the truth about what happened during the Sundering is slowly slipping away.
Connection to the Protagonist
The protagonist's amnesia may or may not be related to obliviasis. Their memory loss was caused by Kumyo Kyo (the 4th Sovereign of Reality and Illusion) sealing them in an illusory world. Whether obliviasis compounds this or whether the protagonist's condition is entirely separate from the broader disease hasn't been clarified.
Darsea and Kumyo Kyo
Darsea was Kumyo Kyo's younger sister. After her death, which Kumyo Kyo is reported to have blamed on the World-Ender, he sealed the World-Ender in the Plane of Illusion as a promise to her, then vanished himself. The brother who controlled Illusion imprisoned the one he blamed in an illusion; the sister whose death unleashed forgetting upon the world. The symmetry is deliberate.
Research into a Cure
The Evolution Test introduces Otto, a young researcher devoted to studying obliviasis. His official profile calls him a young expert in obliviasis research who is not interested in academia, is obsessed with inventing, and is dedicated to uncovering the origins of the disease and finding a cure. Coverage of the test describes him as a Kardia with an Anima named Chimaura. Otto is presented as a face that returning Honkai players may recognize, but his role here is specific to this game and his earlier-franchise history is not part of the confirmed Honkai: Nexus Anima story.