Putting bread in the refrigerator can prevent mold growth on the bread due to the cold temperatures in the refrigerator.
But when you put bread in the refrigerator it tends to go stale and dry out so although you may not have moldy bread by putting the bread in the refrigerator the bread won't be as good to eat as it would be if you left it out at room temperature.
It's best to place bread in a bread box to keep the sunlight directly off of it or leave the bread out on the counter and eat the bread within a few days to prevent the bread from becoming moldy.