The boxes are called double walled heavy duty shipping boxes in North America. Basically it is a two layered box in a box wall construction.

In major US/Canadian cities the best place to get these is at Filipino stores. They are called Balikbayan boxes for shipping/taking stuff during home visits. They are also 20in cubed so at 60 linear inches it fit under all standard airline dimension guidelines. Some of the premium ones have a coating on the exterior which is water-repelling.