By reducing an enemy nation’s Geographic Efficiency you can cause many of its defenses to become inactive, or “inert”. Those defenses will then pose no threat as you push further into their territory. When you attack a square containing an inert enemy defense, the defense will not trigger, and the word “inert” will appear over the square.
Because Geographic Efficiency is so important to a nation’s defensive ability, reducing an enemy nation’s Geo can be a very useful tactic during an attack. This can be done by poking “holes” in the nation’s territories. A common technique is called “checkering” — capturing every other square of a nation’s territory. This reduces their holdings to a checkerboard pattern, which is terrible for Geo. Of course it will be just as bad for your own nation’s Geo to hold territory in that pattern, so while “checkering” another nation you’ll usually want to evacuate each square soon after capturing it.