Corrugations add chordwise stiffness/strength/rigidity (as already mentioned)
at a lower cost than the alternatives: adding a separate structure of stringers or ribs, with rivets to attach a smooth skin; or bonded honeycomb materials.
Cost in both money (materials, assembly labor) and/or weight.
At some point, as aircraft get heavier/faster/more expensive overall - the minor savings of corrugated construction become insignificant compared to other costs in drag, maintenance, total strength. Which is why they are mostly used in small, relatively slow GA planes.
As a side note - SPANWISE corrugations are being explored as a means of controlling/inducing vortices over the wing for aerodynamic reasons (analogies: dimples on a golf ball; stitching on baseballs). I wouldn't expect to see them on your local Airbus/Boeing any time soon - but you just never know....
