The opening crawl of Star Wars: The Acolyte states that the "Jedi Order and Galactic Republic have prospered for centuries without war." While this is true in a broad sense and gives audiences the context needed for The Acolyte, these words gloss over a formidable enemy who greatly threatened the Jedi and the Republic during the High Republic era. These villains created tremendous destruction and suffering across the galaxy.
This enemy is a villainous group of marauders known as the Nihil, who were at the height of their power about a hundred years before the events of The Acolyte. They are the primary antagonists of Phase I and Phase III of The High Republic publishing initiative.
Warning: There are spoilers ahead about the Nihil and Phase I and Phase III of The High Republic.
The Nihil were born out of the destruction of the Jedi-hating cult known as the Path of the Open Hand. With their operations based in the Outer Rim, the Nihil would take what they wanted and kill those who defied them. Between the masks they wore over their faces and their quick and brutal attacks, the Nihil were shrouded in mystery and fear.
Despite their anarchistic philosophies, the Nihil were a structured organization in their own way. They were divided into three tempests, each led by a different Tempest Runner, and underneath them was a hierarchy of Storms, Clouds, and Strikes. The organization also had a symbolic leader known as the Eye of the Nihil.
The first Eye of the Nihil was Asgar Ro, who gave the Nihil Path engines which were hyperdrives that allow a ship to navigate hyperspace through fast and unconventional routes. After Asgar's death, his son Marchion Ro became Eye of the Nihil and continued supplying them with Path engines. Marchion eventually became their true leader instead of just being symbolic, having all the tempests follow his vision.
As the Republic expanded into the Outer Rim with help from the Jedi, the cunning Marchion engineered a plan to have the Nihil fight back against the expansion and gradually destabilize the Jedi and the Republic. This included destroying a Republic freighter in what became known as the Great Hyperspace Disaster, a massacre the Nihil carried out during the Republic Fair on Valo, and sabotaging Starlight Beacon, the ultimate symbol of the Jedi Order and the Republic.
To combat the Jedi specifically, the Nihil unleashed and controlled creatures known as the Nameless, who prey on the Living Force. The Nameless consume Force-sensitive individuals with fear, making it difficult for them to use the Force as they are overcome with nightmarish hallucinations. The Nameless can even kill their victims by turning them into calcified husks.
After the destruction of Starlight Beacon and the growing threat of the Nameless, all Jedi were recalled to Coruscant to regroup. During this time, the Nihil erected a barrier known as the Stormwall through devices known as stormseeds. The planets trapped behind the Stormwall were cut off from the Jedi and much of the Republic, suffering under the cruel reign of the Nihil, with the Jedi and the Republic struggling to penetrate the barrier for over a year. The Nihil also expanded the Stormwall when Marchion dictated it, swallowing even more planets into their territory.
How the Nihil are ultimately defeated remains to be seen, but it will presumably happen by the end of Phase III. They are obviously gone by the time of The Acolyte, and their defeat has been referenced in other stories later in the timeline, including Dexter Jettster's short story "The Veteran" by Adam Lance Garcia in From a Certain Point of View: Return of the Jedi.
Vernestra Rwoh, whose live-action debut was in The Acolyte's first episode, "Lost/Found," has faced the Nihil on numerous occasions, with her early years as a Jedi Knight and a Jedi Master being shaped by the profound hardship and tragedy the Nihil inflicted. While the Nihil won't appear and likely won't even be mentioned in The Acolyte, their history explains a great deal about Vernestra's evolution as a character and as a Jedi since her first appearances in the books and comics.
To learn more about the Nihil, the best place to start is by reading the novel Light of the Jedi by Charles Soule. The novel compellingly introduces these unique villains and lays the groundwork for all the High Republic-era stories that follow.