Foods are very important in DF as well. Same with medical kits, they help you survive. If you don't eat any food you will starve to death. The more hungry you are, your health points will start to decrease! It could also effect your Exp. Same with medical kits the higher the level the better food you'll need. Foods can be looted in the city as well.

Hunger Indicators:
Nourished 100%-75%
Fine 74%-50%
Hungry 49%-25%
Starving 24%-0%