It didn't really give any background, save for a few words on screen to sort of set the scene. I've read several articles about the movie since and the director essentially was not looking to make any kind of typical war movie - no heroes, or grand speeches, or huge acts of bravery. The entire movie takes places within 36-48 hours of the most intense time of evacuation from the beaches. There's actually really not a ton of dialogue either. No back stories of soldiers' lives or families are given. It's strictly the very NOW...the reactions to what's going on right then and there. It's the British and French soldiers all over the beach and the chaos of attempting to get them on ships and get them home all while enemy planes are taking out their ships as they try and leave. It focuses on the desperation and the helplessness of these soldiers trying to do anything to get off that beach. And of course the civilian boaters coming to their rescue.
I strongly suggest seeing it in the theaters, unless you have an impressive surround sound at home. The noise is carefully created to make you feel like you're on that beach. I had to cover my ears a couple times. I'm not kidding about it's intensity but I realized after, the purpose and importance.
I'm close to the generation you're talking about but I've always enjoyed history, and my father is a huge military history buff. Before seeing the movie, I admittedly knew very little of the Battle of Dunkirk, knew it was an important point in WWII but that was about it. I've enjoyed researching it more in depth since seeing the film.