“German nation bonus earned after winning a battle.”
Teutonic Fury is a specific battletactic that only the Germans possess. After a multi-player or war victory it gives you a 15% attack boost towards your next attack (for all of your troops/planes). This is repeatable and you can keep this booster as long you keep getting a star, however once you lose a battle you will loose the booster and will have to win another battle to regain it. This tactic carries over towards war as well.
See if Teutonic Fury is active by checking the information for a barrack, factory, or airstrip; there it will tell you if your troops/planes will do 15% more damage. Not saying this means it is not active.
It only applies to offense.