Transcendence
The Transcendence refers to an instantaneous, worldwide event that took place when the Twins were twelve. The barrier around Gravity Falls keeping in the supernatural properties shattered and allowed it to spread across the globe and changed the course of human history.
Origin
For thousands of years before the Transcendence, the dream demon Bill Cipher had been planning and setting up a massive and complex spell. This spell was designed to merge together the separate Mindscape and physical plane into one. This would cause widespread chaos and tragedy throughout the world and bring human civilization to it's end. Not being inherently good or evil, Bill Cipher simply wanted to have fun and laugh at the chaos his spell would bring to the world.
Being one of the most powerful beings in the universe, he altered human history and steered the civilizations of earth in the right direction to make reality the precise way he needed it to be for his spell to work. Waiting for the right movement when all of the universe had aligned to unleash it's power. After thousands of years of work, he did a small test run 30 years before the Transcendence, opening up a small sliver of the Mindscape and contained it within the small town of Gravity Falls.
Dipper and Mabel Pines had followed the clues left behind and formed a small team of friends and others who knew of the supernatural occurrences in town to try and stop his plan from following through. In the end they just barely managed to defeat him and saved the world from the disaster his spell would have caused. However, the spells backlash went not only to Bill but also to the barrier surrounding the town and keeping in the sliver of Mindscape. With the barrier shattered, the whole world was plunged into confusion and upheaval as supernatural occurrences appeared around the globe.
The Aftermath and Dippers Predicament
Immediately after the spell was stopped, most of the backlash of it's power went directly to Bill. Causing him to loose much of his power and left him just barely clinging to life. In order to survive, he made a huge gamble on his part, forcefully possessing Dippers body. A demon as powerful as him could do it without a deal, but in his weakened state there was a high risk that we would fail and die in the process.
While he had the bonus of inhabiting Dippers body before, he still was not strong enough. Dipper fought against the possession with all of his might and in the end, Bill could not win. He dissipated and his energy merged with Dipper, effectively pulling him into the Mindscape and making him a demon as well.
Post-Transcendence Civilization
While society initially reels from the supernatural occurrences spontaneously popping up all over the world, Gravity Falls remains largely unaffected, being pretty used to such things already.
Eventully, the rest of the world developes a basic idea of what happened during the transcendence, and come to recognize Gravity Falls as it's epicenter. School systems around the country begin to implement new courses designed to inform children about the supernatural in general, as well as the dangers such things potentially pose.
New political parties are formed in response to this new influx of supernatural exposure, such as the Pro-Nats (Pro Naturals), whom tend to be against equal rights or affirmative action for beings of magical origin.