Insurgencies are a feature in the game that is automatically unlocked after you complete the main storyline.
Despite the death of Anton Castillo, devout remnants of his regime still believe the True Yaran cause. Every week, a province from the map (Ex: Barrial) will be taken over by an Insurgency. At first they will appear as "[REDACTED]", but as you capture objectives (checkpoints, military bases, and anti-aircraft cannons), more of the location will be revealed. After it is completely filled out, the map will display the Insurgency leader's name and where to find them. From there, take over the base and kill everybody. Successfully killing the leader will result in the Insurgency being crushed. Insurgencies reset weekly.