RORY: I’m jumpy. On the Fourth of July, forget it, I’m a wreck. And when the Stars Hollow orchestra begins to play in the gazebo, the guy banging the cymbals, I’m . . . it drives me nuts.
Fourth of July is the date of Independence Day, and often used colloquially as its name. It’s a federal holiday in the US, commemorating the signing of the Declaration of Independence from Britain on July 4th 1776. A day of patriotic display, music, fireworks, and mid-summer picnics and barbecues.
We never get to see the Fourth of July in Stars Hollow, but of course they would have the same sort of celebrations as elsewhere. Presumably it is the fireworks which make her “jumpy”. Rory tells us that there is a town orchestra who plays in the gazebo on this date – which means the orchestra must be small, that they all fit in the gazebo.
The Annotated Gilmore Girls 