The Rikers are former inmates of the Rikers Island Correctional Facility in New York City. Seizing on the chaos of the Dollar Flu and the lack of prison guards willing to work through the outbreak, Larae Barrett unified the various prison gangs and convicts into a force capable of taking control of large swathes of Eastern Manhattan.
Intel
The Rikers formed during the later days of the initial outbreak, when convict Larae Barrett seduced the prison warden and managed to convince him to arrange for a barge to come to the island so the two could escape together. As the prisoners rioted and broke free, Barrett killed the warden and led the way into Manhattan. This was essentially the straw that broke the camel's back, as the JTF's withdrawl from the center of Manhattan and creation of the Dark Zone along with initial chaos had cost them much of their forces. With the arrival of a well-organized and dangerous army of criminals, the JTF had lost what little control of Manhattan they could claim they had.
The Rikers proceeded to celebrate their success, going on a rampage of killing JTF personnel and becoming modern-day highwaymen to the remaining civilian on the streets. Using captured weapons from the JTF and presumably further weapons found on the black market and through their criminal connections. More concerning was Larae Barrett's sheer force of will and charisma, uniting the prisoners into a unified force focused on seizing what was left and becoming kings of the city.
Being seasoned criminals and killers, the Rikers are a step above the Rioters in terms of both gameplay and cruelty. Where the Rioters can argue that they do what they have done to survive in a collapsing city, the Rikers outright state that they're seeking control and revenge. Graffiti scattered through their territories reinforces this; "Fuck#Justice We Want Revenge", "Twelve Years in Rikers; One Cop for Every Year", and various other statements on their goals. Their neighborhoods are even "decorated" with the posed and hung bodies of JTF soldiers and police they've captured, and they are often seen in the streets beating on civilians and JTF personnel.
Eventually, however, the agents manage to break through to the Rikers' "headquarters" at the Lexington Event Center. Finding the bodies of several recently killed JTF agents in a dining room along with an ECHO showing the sadistic means by which the Rikers murdered the men and women, from forcing two men into a drinking contest using drain cleaner to threatening a man with death if he didn't play a song properly on the piano when he had no knowledge of music at all Money and champagne bottles are scattered everywhere, reinforcing the fact that the Rikers are more concerned with partying through the fall of the city than survival. Moving through the building and eliminating the leadership of the Rikers, the Division finally neutralizes the Rikers as a serious threat to Manhattan.
Killing Barrett doesn't eliminate all the Rikers however, as one group seizes control of the WarrenGate power plant and attempts to blow the facility under the belief that since the outbreak, nothing else matters except what they can do. Another force seizes a Last Man Battalion SAM site, and begins shooting down SHD supply helicopters. While the Rikers may have been broken, clearing them out of Manhattan entirely will be a long and bloody task.