Hunger is one of the two motives medieval Sims have. It indicates their need (and sometimes desire) for food.
Throughout the day, a Sim's Hunger will fall at a steady rate until they begin to get Hungry. Sims who continue to not eat will eventually become "Very Hungry" (-40 Focus). Eventually, a Sim who hasn't eaten will starve to death. It takes approximately 9 hours and 25 minutes for a hero's hunger to go from full to hungry.