The breadbox for your bread does keep the bread fresher longer because the breadbox creates a dark environment for the bread.
When the bread is stored in a dark environment it stays fresher longer than being out in the light and mold doesn't grow on the bread as fast in a breadbox.
Still the heat and humidity in your home could cause the bread to go bad even in the breadbox.
So while the breadbox can help keep the bread fresher longer it's still doesn't meant that it will always last longer in the breadbox.
You can store bread in the refrigerator which helps it last longer as well.