For a generation of Americans, June 6 is a day that they won't and can't forget. June 6, 1944 saw the largest amphibious landing in history (up to that time) take place at Normandy. Until that day, the term D-Day was the generic term for the beginning of any major military assault. It's still used that way, but mention D-Day to most people of a certain age and this is the one that comes to mind.
There are some good Internet resources on the story at the National D-Day Museum and the National D-Day Memorial. Heck, just put "d-day" in Google and you'll get 1,580,000 pages back.
The stories you'll read on those pages are simply staggering. Those of us who have never had the dubious privilege of fighting in a battle will never be able to understand what these men went through. (And no, watching Saving Pvt. Ryan 18 times most emphatically does not give you a good idea of what it was like. Idiot.)
If you know a WWII vet who was there, you owe him a handshake and a thank you. If you're really lucky, he might tell you a story or two in return.