Hunting: Survival quests are one of three different hunting missions in the game, which will require you to hunt some animals. These differ from the others, in that, you will need to protect some civilians from animals trying to attack them. In order to pass, you will have to make sure that at least one civilian lives until the end of the mission.
There’s a total of six Hunting: Survival missions in the game, which are unlocked upon liberating outposts. Nothing substantial is really unlocked by completing them, but you do get Rupees bonuses for finishing three and all six missions.