Starvation occurs if the player does not eat food over a long enough period of time. It accumulates slowly at all times, and primarily affects Strength, though Perception and Charisma also suffer at higher starvation levels. It takes five days for the player to starve without eating anything. Most types of food will reduce starvation by some amount, though certain foods are more effective than others.
Consumables cannot actually make the player character more hungry, they can only reduce it or leave it unchanged. The amount of food an item provides is not related to its weight, value, or any hit points restoration, determined by separate properties. The Survival skill is the greatest asset, as it scales the amount of sustenance an item provides.
MREs in Lonesome Road are perhaps the most convenient item for avoiding hunger, as they restore upwards of 600 points (more than half the range) and are lightweight, cheap, and plentiful in the Divide.