The war most American schoolkids have continuously hammered into their brains, without really understanding.
In brief and colloquial terms for slow-witted teens:
Colonists were pretty pissed off at mama-san Britain for the policies she created after the French & Indian War, so toss in a shitload of taxes and acts, and you've got even more rage. Colonists start getting bratty in regards to paying the taxes and obeying the acts they see as unfair, and British throw even more at the bastards, without warning. Now REALLY angry, colonists start banding together thus boycotts and protests (think Boston Tea Party) erupt. Thomas Paine steps in with "Common Sense" and says "Hey, colonial dudes, independence from the Brits = pretty sweet idea." At first people call him insane, but soon enough THE WAR BEGINS. Yada yada Loyalists and Patriots yada George III. Ben Franklin goes to France and gets them to help the colonists out. Brits first seem to take the lead. Colonists eventually regain strength and topple Brits in the end. July 4th, 1776 = Declaration of Independence, among other things, but hey man, THE WAR WAS STILL GOING ON WHEN THEY WROTE IT. Articles of Confederation (American Constitution Sr.) is pretty much the nail in the Brit/Colonial connection coffin.
Voilà. A new nation.
note: I'm not a professor, so this of course is not some exact, blow-by-blow description of the war.
I hope you now change your definition of the Revolutionary War, American. Better cross out that "Yeah, the British were like TOTAL DICKS, so we were like FUCK THAT, WE'RE AMERICA, so we fought 'em. Wait, England = Britain, right?"