Mitochondrial inner membrane
There is a reasonable speculation. That is to get more areas where ATP synthases are localized in order to produce ATP. But this doesn't tell why the structure has to be the exactly that shape.  

As the review Ilan show, the shape seems to be determined by ATP synthase dimerizetion. The shap may be just a consequence of ATP synthase dimerizetion, although it successfully enlarges the area where ATP synthase is localized.