Hunger is one of the basic measurements in the game, ever single consumable food item the player comes across can fill up this meter and satisfy their hunger.
If the player were to starve themselves in the Story Mode, they will not die from it. Instead they'll have part of their stamina bar cut until they consume food again.
Starvation in Survival or Sandbox mode however, will make the player go through the process of dying. Giving them a few minutes to consume food before eventually keeling over and dying.
In the DLC's, Hunger is disabled, this is due to survival not being the main focus of those modes, so food is then turned into health items that will increase each character's health.
Status Effects Edit
Some of the food items also do more than just filling up the hunger.