Cardboard boxes are not made of flats sheets of paper. The sides of cardboard boxes consist of of a rippled sheet of paper on either side of which are flat sheets of paper. The rippling of the sheet of paper in the middle makes the whole structure more rigid (top diagram below). This structure however will easily bend in one direction. The structure in the top diagram below will easily fold by lifting the left and right hand sides.
The structure can be made more rigid, and rigid in any orientation by making many layers of paper and corrugated paper on top of one another.
Corrugation makes it possible to make light, strong structures. Rooves may be made from corrugated iron, and structures may be designed to collapse safely by having corrugations built into them. Corrugations make it possible in some circumstances for energy to be gradually absorbed by a structure, allowing a more orderly collapse and more warning of collapse.