The Hunger is one of Abaddon's minions and in service to Varesh Ossa. While only one of many demons at Varesh's disposal for bringing about the Nightfall, it is the only one that speaks during cinematics. It is likely named for its intense appetite for meat (alluded to in the quest Herds to the Slaughter). The creature, like Varesh herself, seems to share a bond with other demons, most notably The Drought.
The Hunger constantly spams Hunger's Bite to inflict multiple conditions and steal health from a foe. Note that Hunger's Bite can not be disabled, and interrupting the skill is not effective due to the 0 recharge time and inability to disable it.
Despite its size, the Hunger can be knocked down. Lightbringer's Gaze also works well against The Hunger.
It is strongly implied by multiple NPC's throughout Kourna that the enemy soldiers are taking a great deal of meat from citizens, and several soldiers keep "going missing" overnight. These ominous suggestions almost surely point to the Hunger devouring as much meat as it can, even from its own allies (which few, if any, of the demons show any concern for).