What is Oblivios
Oblivios 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.
Origin
Darsea was killed by the World-Ender. 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. Oblivios 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 Oblivios. Their memory loss was caused by Kumyo Kyo (the 4th Sovereign of Reality and Illusion) sealing them in an illusory world for over 214 years. Whether Oblivios 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 she was killed by the World-Ender, Kumyo Kyo sealed the World-Ender in the Plane of Illusion as a promise to his dying sister. Then vanished himself. The brother who controlled Illusion imprisoned the killer in an illusion; the sister whose death unleashed forgetting upon the world. The symmetry is deliberate.