June 6, 1944, saw the storming of the beaches at Normandy by the Allied troops. According to the eNotes article (link below),
"In the Normandy campaign, the Allies destroyed a substantial portion of the German forces in northwestern France. This led to the liberation of Paris (August 25) and the remainder of France, which put the Allies in position to advance into the Low Countries and ultimately Germany itself."
This was huge - It not only gave the Allies a much-needed victory in Europe, which allowed them to have a strong foothold on the continent, but it also gave the people of Europe, particularly Jews in hiding like the Franks, hope that they might survive this horrible war.
Another link to check below concerns the themes of "The Diary of Anne Frank," one of which is the fact that Anne was a very hopeful, optimistic person. Despite the horrors she heard about on the radio, she still maintained optimism about the world and the future. The invasion of Normandy would have added to her sense of hope for the future.
The most immediately applicable event, involving thousands of soldiers and considerable equipment, is the invasion of Normandy. It was both symbolic and strategic; it was a sign that the Allies really would win World War II.