The Shadow Council seen on "The Mandalorian" is actually the second iteration of the group, rebuilt after it essentially imploded in on itself several years prior. As far as a brief summary goes, the council was originally developed by Emperor Palpatine's right-hand man Gallius Rax as a way to maintain the spirit of the Empire after the death of its biggest leaders. The group was somewhat successful, managing to rally the disparate Imperial forces into a singular body once again, but that's not the full reason Rax created the group.
As it turns out, Rax had orders from Palpatine to enact a contingency plan in the event of his death that essentially amounted to gathering the remaining Imperial forces, slaughtering them, and rebuilding the Empire completely from scratch with only the most devoted being granted survival. The leader nearly accomplished this goal by attempting to blow up the planet of Jakku with the whole of the Empire on it under the guise of a battle with the New Republic, but he was ultimately thwarted and killed.
"The Mandalorian" not only reveals that the Shadow Council has reorganized after this defeat once again, but some original members like Brendol Hux are still leading the charge, in addition to fresh faces like Moff Gideon. However, without Rax at the helm, fans can only guess at what new plans the group is cooking up in service of the Empire.