August 15, 1945 (August 14 in the US) is when World War II ended. August 6th and 9th were the dates America dropped the two atomic bombs on Hiroshima and Nagasaki, respectively.
These dates really meant nothing to me living in America - yes, I definitely learned about them in history class, but Pearl Harbor and D-Day are the most memorable events as taught to me in school. And while there's no talk here of Pearl Harbor, every year I hear about the bombs in early August.
While I'm on the topic, the master recording of the Japanese surrender was just officially released last month; you can listen to a copy below in a video from 2011: