Cardboard packing boxes are great for moving, storing, and shipping just about anything that will fit inside them. But as handy as they may be, they are not suitable for just any task, and they are not able to withstand some very specific punishments. One thing they are especially susceptible to is moisture.
Obviously, most of us understand that if you leave a packing box out in a pouring rain you'll retrieve it later only to find it completely useless. The water-softened cardboard has lost all its shape and strength. Even given time to dry, it may be adequate for a use or two, but its integrity has been compromised to the point of simply discarding it. However, there is another moisture threat that's not so obvious. It comes in the form of a slight dampness in a garage or basement; dampness that doesn't soak cardboard but can be equally damaging.
Cardboard is a very porous material to begin with. Add to that the fact that packing boxes are made of corrugated cardboard, which is made up of fluted panels, and you have a great place for mould to grow if conditions are right. That's where the damp basement or garage comes in. If you're using cardboard packing boxes for storage purposes, and your storage area is damp, you could have mould growing in your boxes very quickly.
The best way to avoid it is to use plastic storage boxes and metal shelving. Mould has a more difficult time growing on a plastic surface, and the shelving will keep the boxes off the floor. Between the two you should be able to keep the mould potential at a minimum; if you do find a little beginning to grow you can kill it with chlorine bleach.