Foods are items that refill your Hunger Bar, and add a layer of saturation to it. The Hunger Bar is the line of "chicken nuggets" (actually called Shanks) above your in-game hotbar to the right.
If your Hunger is at at least then your Health will regenerate x0.5 every 5 seconds. If the Hunger Bar is reduced to 0 (no Shanks are colored in), you will start losing Health; to x5 in Easy Difficulty, to x0.5 in Normal and down to x0 (dead) in Hard.
To eat, simply select a food item in your hotbar and hold your right mouse button.