The Breen Imperium was the interstellar state of the Breen during the 32nd century, and a successor to the earlier Breen Confederacy.
The Imperium was adversarial to the Federation. As of 3191, they were occupied by infighting over their leader. The escalating conflict between the factions worried nearby Federation worlds, which requested additional defenses. (DIS: "Red Directive", "Under the Twin Moons", "Jinaal", "Erigah")
The Yod-Thot were involved in this power struggle, with Ruhn mentioning that the Yod-Thot were campaigning for the throne of the Imperium despite having royal blood. The civil war was fought between six Primarchs of the royal bloodline -- including Ruhn and Tahal -- all trying to claim the throne of the deceased Breen Emperor. L'ak, as the descendant of the Emperor and Scion of the Breen Imperium, was the Imperium's rightful ruler, but he didn't want the throne. Control of L'ak bolstered the claim of the faction that he was involved with, but L'ak abandoned the Breen for his love Moll. (DIS: "Mirrors", "Erigah")
Ruhn was later killed by Moll who rallied his forces to her cause to resurrect L'ak and place him on the throne of the Imperium. However, this caused the five remaining Primarchs to move to solidify their claims to the throne with Tahal chasing down Ruhn's dreadnaught to claim his forces for herself. Federation Ambassador Saru, who had been on a diplomatic mission near Breen space shortly before this development, warned that news of this would cause panic on the nearby Federation worlds. Although Ruhn's ship was severely damaged by the USS Discovery, most of Starfleet was too far away to help against Tahal who was coming with her whole fleet and posed a significant danger should Tahal get her hands on the Progenitors' technology. (DIS: "Lagrange Point")
Tahal's attempt to take the Sixth Flight for her own was ultimately foiled by Saru who intimidated the Primarch into backing down. Both Ruhn's dreadnaught and a scout ship sent by Tahal were sent to the galactic barrier by Discovery where they would take a couple of decades to return to Breen space. However, Captain Michael Burnham learned from a Progenitor that it was impossible to resurrect L'ak using the technology, ending any hopes of placing him on the Imperium's throne. (DIS: "Life, Itself")
In an alternate timeline where the Imperium obtained the Progenitors' technology from Moll and L'ak, they launched a devastating assault on the Federation, destroying Federation Headquarters and disabling the USS Discovery. According to Zora, the Breen destroyed "everything." (DIS: "Face the Strange")