Before we start, let's not forget what the Nazis believed: their superior race should dominate while all others should be subservient. Their crazed leadership pushed that agenda through systematic brainwashing, using force, brutality, and sheer terror to ride herd over the sanctity of life. A nation's sovereignty and its citizens individual liberties were irrelevant to them.
By 1944, the Nazi regime's borders had expanded through most of Europe, and France had fallen. Britain stood alone as the last European holdout against Nazi occupation. Only the English Channel and a strong RAF stood between England and Hitler's forces.
General Eisenhower and the other Allied commanders knew they couldn't let England fall to the Nazis. So on June 6, 1944 over 160K Allied troops landed along a stretch of coastline in the Normandy region of France. Their purpose: to push against the heavily-fortified German forces and regain France.
Over 5,000 ships and 13,000 aircraft were involved in delivering and supporting the soldiers as they began the push inland along 50 miles of coastline. More than 9,000 Allied soldiers were killed or wounded, many in that first wave. 
As we know now, the end result of this incredible effort was the ultimate defeat of Hitler and his regime. Of course, the soldiers involved couldn't know that at the time.
All they knew was that they were fighting against an evil that held one type of person as dominant over another. They were fighting to ensure that the people of Europe would have what we Americans purport to believe: that all men are created equal and are endowed by their Creator certain unalienable rights.
Yep, this is a good time to remind us of what the writers of the Declaration of Independence said are 'self-evident.' We are indeed all created equal.
