Your Food meter is a representation of how well fed your character is. Eating food increases it, which in turn increases the rate you regain <a action="GoToPage" data="Mechanics_Vitals">Health</a>. Running out won't kill you, but if it gets too low you won't heal over time at all anymore. It's important to keep this meter high in order to keep going after a fight.
The easiest sources of food are Berries found on bushes and simple Cooked Meat made at your camp from meat harvested from dead animals.
Similarly, your Drink meter is a representation of how well hydrated your character is. Drinking increases the meter, which improves the rate you regain <a action="GoToPage" data="Mechanics_Vitals">Stamina</a>. Even with an empty drink meter, your Stamina will still regenerate. However, having a high Drink meter will make sure Stamina refills quickly, and can be the difference in a tough battle.
The easiest way to refill Drink is simply from Fresh Water. Find a river or lake, collect some, and drink up.