Humidity is important in a breadbox because it helps maintain the integrity of the bread. In general, breadboxes are made out of wood and as a permeable substance it allows for the cultivation of moisture. The moisture in the bread increases the humidity in the breadbox and keeps the bread moist.
Air circulation is important for keeping the bread from getting soggy from too much moisture. The humidity and air circulation coupled together create the perfect amount of humidity to keep the crust of the bread crisp and the interior of the bread moist.
From the humidity and air circulation, a consistent temperature is achieved. This helps deter the formation of mold, if only for a few days.