For a lot of casual fans, the First Order kind of came out of nowhere in The Force Awakens, almost like the filmmakers wanted a reason to keep having stormtroopers, even though they shouldn't have been around anymore. Since, you know, they were basically Ewok tom-toms at the end of Episode VI.
Well, as with anything Star Wars, there's a lengthy backstory now as to how the First Order came to be, and it all started with General Hux. In both The Force Awakens and The Last Jedi, Hux (Domhnall Gleeson) serves as the order-shouter, the head military honcho who essentially took the place of Moff Tarkin. But the behind-the-scenes extended stories describe how Hux was a child when the Empire was defeated. He traveled into exile with his father and started cultivating what became the First Order using the ideology of the defunct Empire.
As detailed in the novel Phasma, Hux's power within the blossoming First Order continued to grow, and he eventually concocted a plan to assassinate his father (although Captain Phasma did the deed). About ten years after that, Hux was a general in charge of Starkiller Base, and the rest is cinematic history. But judging by the meager screentime he gets, fans probably wouldn't guess that Hux is the reason the First Order is around in the first place.
And while we're on the topic of the First Order…