War has social, political, as well as military dimensions. It doesn't have to be a battle but it must be a turning point and it must be a specific war.
The atomic bomb. Marked the end of the era of direct total war that plagued the first half of the century; and unleashed an era of indirect total war(aka Cold War) that over-shadowed the second half.
Overall WWI and WWII were the major turning points of the century. Without them, much of the 20th century wouldn't have occured.
Again, I am not looking for Wars themselves as turning points but a specific war, with a specific turning point in it, be it within a social, political or military context
Definitely the battle of Amiens, this was the first taste the world got from the future of warfare.
Tanks broke trough lines that would have been impenetrable for infantry, planes worked in support of the ground forces, warfare became mobile once again.