score:13
He is referring to World War II, when the USA (and the UK, as well as many other countries around the globe) were on the same side of global conflict as the Soviet Union (allied against the Axis powers -- Germany, Italy, and Japan).
...just as men from Boston and Birmingham risked all that they had to storm those beaches and scale those cliffs...
That invasion would be Operation Overlord, the US / UK / Canadian invasion of Normandy in June 1944.
The cliffs scaled is a reference to the action at Pointe du Hoc.
...Soviet soldiers from places like Kazan and Kiev endured unimaginable hardships to repeal -- to repel an invasion, and turn the tide in the east.
That would be Operation Barbarossa, the German invasion of the Soviet Union in June 1941.
As for the unimaginable hardships, in the USSR alone about 27 million people lost their lifes. The video The Fallen of World War II does a very good job visualizing the staggering losses.