It wasn't until I wrote Chronicles of An Academic Predator and 1968 that I really understood the significance of this holiday. I lived in my white-bread suburban world, aware of racial issues and tensions, but not impacted by them, at least not significantly. Then I read about the civil rights movement (riots in Birmingham, the Freedom riders, etc.) as part of the research for those two stories, and was amazed at the courage and fortitude of the people of all races, but especially African-Americans, who fought so hard for change. They really did blaze the trail for the gay rights movement, and the fight for fair treatment for the GLBT community that persists today.
If you have a spare hour to kill, go to Wikipedia and type in "1962". It will give you a summary of the events of that year. Follow it through to 1968, at least. I think you'll get a feel for what I'm talking about.
If you do, take a moment to note the change in tempo and violence as the movement shifted it's focus from the South (early 1960s) to the North (latter 60s).