Point of Divergence

A point of divergence is a specific event in an alternate history story that occurs differently than it did in factual history. Most alternate history authors will change a single event, creating a "ripple effect" that sets up the scenario. This divergence, which acts as the story's "unicorn in the garden" or "one big lie", may range in importance and realism from a character dropping or not dropping a piece of paper at a crucial time, to time travel and alien invasion (such as Harry Turtledove's "Balance" series, when World War II is interrupted by a fleet of lizard-people from outer space).

Examples of Point of Divergence include:

Film

Captain America: The First Avenger shows what happens when Allies and the Axis powers alike try to create a super soldier. You can see the point of divergence is when Steve successfully completes the experiment The Allies succeed, and the Axis powers opt to find a mysterious blue cube that can improve weapons development instead until Dr. Zola succeeded in making Bucky Barnes Nigh Invulnerable before brainwashing him into becoming the Winter Soldier. While Howard Stark fails to use the Tesseract to generate any powers, SHIELD learns it can power fighter jets, and Tony gets inspired by his father to develop clean energy using a larger version of the Arc Reactor.

Literature

In Witch Week, a book in the Chrestomanci series, it turns out this parallel universe of witches, prosecution and rampant magic was created because Guy Fawkes succeeded in blowing up the House of Parliament. Simon, one of the few non-witches, was cursed that anything he said would no longer be true, so he utters that Guy Fawkes did that. It ends up undoing the magic and merging that universe with our world, setting history right. Chrestomanci sighs in relief and leaves the kids to celebrate Halloween.
Scott Westerfeld's Leviathan shows how World War I would have been kicked off much sooner and with more consequences. How? Charles Darwin discovered strands of DNA along with the theory of evolution, and he had the means to learn to create beasts by manipulating the helixes. An arms race ensues because the British are making giant living warships, while the Austrian-Hungary Empire focuses on robotics. Alex, instead of being one of many siblings, is an only child and orphaned after his parents Archduke Ferdinand and Catherine are killed, and the Russian Revolution never happens.
Dean Koontz's Lightning asks, "What if the Nazis had discovered time travel, and there were high-level resistance members seeking to ensure that Nazis never win World War II?" You get a bunch of time-traveling Nazis that decide to go after a woman in the 1980s that one of the Resistance members keeps saving.

Live-Action TV

In The Boys, this is how Supers emerged. A Nazi scientist defected during World War II with his wife, later revealed to be Stormfront and founded Vought to profit from pharmaceuticals and build superheroes. Frederick Vought received a pardon from the US government to develop Compound V, and turned Supes into an entire industry where his company would manufacture heroes, and ideally super soldiers. As a result, there are no Marvel movies and Vought is the major corporation in the United States for entertainment, heroes, and merchandise.
Abed references this trope in an episode of Community where Jeff rolls a die to determine who will get the pizza for the study group's party. He says six different timelines can ensue, though Jeff rolls his eyes before tossing the die in the air. While things are okay if Annie, Pierce or Britta get the pizza, with Troy and Britta becoming Happily Married in one timeline, things become sad if Abed goes, and downright Nightmare Fuel in the timeline where Troy gets it. Fortunately, only one timeline happens in canon: Abed catches the die and reveals that since there are seven of them, Jeff devised a system where he'd never have to get the pizza. Jeff gives a low chuckle as the group playfully calls him out and send him to grab the pizza as his punishment.
Doctor Who
- In the "better" world in "Doomsday," where Rose's dad Pete is still alive and successful in his business ventures, he explains that the Cybermen invasion was their divergence from the prime universe where Rose is the protagonist with Ten. After the chaos, the British government took control of Torchwood and made it more hospitable, rescuing the Doctor from Prime Torchwood. They use their portals to get rid of the Cybermen and the Daleks before they can destroy Earth Prime, and seal the breach because it's too dangerous to keep the portals open, given it's rapidly accelerated global warming by months rather than years. Rose is then faced with the Sadistic Choice of either being in a world where her mother and father are alive together, or being with the Doctor and separated from her family.
- Parallel Pete himself is a divergence. Rose knows him as her dad who died young and poor, and the greatest dad she knew. Unlike Prime Pete, this Pete found success with his ventures and inventions, and he never had children with Jackie. While he claims he's not father material when Rose reveals who she is and tearfully calls him "Dad," he bonds with her nevertheless and is teary-eyed on realizing that her mother is alive, after losing his Jackie in his debut episode.
Like in the video game, we see that the point of divergence in The Last of Us is when the Cordyceps virus mutates such that it can infest humans, turning them into mindless zombies. While southern Texas is prepared, the rest of society isn't, and as of 2023, the whole world is a wasteland. One Indonesian scientist advises the government to raze the mainland and leave no survivors, because she can see how fast the spores spread. No more elections, no WiFi, and definitely not television anymore.

Video Games

The Civilization franchise makes these points of divergence more complicated than simply changing one fixed point; the player can manipulate different parts of the game to achieve their desired result. You can play many nations and make them the most powerful in history. Gandhi may even get into nuclear weapons and violence!
The Last of Us shows that in 2003, the fungus Cordyceps evolved into a mutant strain that turns people into mindless zombies. As a result, society has completely broken down by the time the game starts, to the point that Ellie in the DLC doesn't know what an arcade is.
It's unknown as of 2023 what the timeline divergence is specifically between Undertale and Deltarune since the start of the latter game greatly resembles the Golden Ending of the former, but the monsters don't know each other. A point of divergence did happen, though, as you can find references to "DETERMINATION" in Deltarune's second chapter while nudging Alphys and Undyne together.
Where in Time Is Carmen Sandiego? is all about how Carmen sends her crooks to specific parts of history to steal important relics and cause these points, for the fun of it. As a time sleuth, it's your job to get history back on track by helping complete puzzles.

Western Animation

In The Batman, Clock King's origin starts from him being jailed for a disproportionately long time because a petty theft attempt went wrong, and the trauma made him reverse time by a few seconds. The Bat family pities him when they hear his story, but they try to stop him from gassing all of Gotham City. Murdering his own son by accident causes Temple Fugate to overload his powers, reverse time, and return to the point before he stole the watch. He decides not to do it, never gains his powers, and becomes a respected clock repairman, starting a family business with his son.
Danny Phantom
- In the Dark Danny two-parter, an older Valerie and Dark Danny reveal to Prime Danny, Tucker and Sam that their Bad Future in Amity Park happened because Danny was caught cheating on a career test, leading to his family and friends being at the Nasty Burger when it exploded due to the teacher bringing them there to make an example of Danny. An older Vlad goes further to say that out of mutual grief and guilt, he helped separate human Danny from his ghost self, only for the ghost to kill the human, remove Vlad's ghost powers, and go evil. Clockwork at the end of the episode gives Danny a chance to avoid this divergence. Danny hands the folder of test answers to the teacher before the test starts, apologizes, and accepts his punishment of detention. Crisis averted, and he learns that Jazz knew about his Phantom side all along.
- In another episode, Vlad blackmails Danny to cure his ghost acne by infecting Tucker and Sam, forcing the Fentons to quarantine them. Danny attempts to convince Clockwork that if Vlad never suffered the accident that gave him ghost powers, then it would save Sam and Tucker and maybe Vlad would become a better person. It would be sound logic, except that Danny by saving Vlad means that Jack gets hit by the malfunctioning portal instead and gets the ghost powers. Vlad is also worse in this timeline; he gaslights Maddy into thinking Jack would hunt them down for the accident, so they become married cheese farmers for twenty years. Maddy has to do ghost work in secret; when she sees Danny's ghost form, since he and Jasmine don't exist in this timeline, he explains what happened and Vlad busts them. When Maddy witnesses Vlad kill Jack in ghost form, she angrily tosses Vlad into the ghost zone before helping Danny return to Clockwork and reset the timeline.
Time Squad is all about this, where the title characters find out how to get history back on track for significant historical events. At one point, Eli Whitney didn't invent the cotton gin but robots instead, and they have to convince him that sorting cotton would be much safer.