Hostage Rescue quests will unlock upon liberating outposts, and require you to rescue at least two of four hostages that have been kidnapped by the Royal Army. All you have to really do is kill all of the enemies in the area with the hostages to finish the mission. The bad part is that you want to use stealth, as the enemies will start killing the hostages if you’re detected.
There’s a total of 14 Hostage Rescue quests in the game, with the biggest reward being the Cannon signature weapon unlocking in the store after finishing five of them. You can also unlock the No One Left Behind trophy/achievement for rescuing 15 hostages, which should happen automatically if you try and finish them all.