Independence Day, more commonly known as the Fourth of July, was a national independence ritual that was celebrated in the United States of America on Earth, and commemorated the adoption of the Declaration of Independence from the United Kingdom on July 4th, 1776. The day was typically celebrated with gunpowder-based firework displays across the country.
During his debriefing about the USS Enterprise's mission to the galactic edge on Starbase 33 in late 2265, Captain James T. Kirk remarked to Admiral Saylor and Captain Francis Damion, that Gary Mitchell and Elizabeth Dehner had "lit up like sparklers on the Fourth of July" when the ship encountered the galactic barrier. Not being native to Earth, Saylor was unfamiliar with the expression and the reference was explained by Captain Damion. (TOS - My Brother's Keeper novel: Constitution)