Fullness drops with time and effort. When starving, you no longer regenerate, you slow down and you lose HP. When well fed, you recover faster.
Dishes are prepared at the stations: campfire (grilled food), oven (bread, flatbreads, pie), kitchen (stew, soup, pancakes, omelette), drying rack (dried meat), salting tub (salted meat, with salt). The more elaborate the dish, the more filling it is.
The bed can be built or bought as a kit from Pïo; click it to sleep: you recover your HP quickly and get less hungry.
See also: recipes.