Ah yes....July 4th....
Independence Day, as defined by Wikipedia, is "a federal holiday commemorating the adoption of the Declaration of Independence on July 4th, 1776, declaring independence from the Kingdom of Great Britain."
See, basically, the Thirteen Colonies had been at odds with Great Britain for a while. Great Britain had this idea of what it wanted The Colonies to be, and the Colonies did not agree with this plan. Additionally, the Empire was trying to survive and maintain its control, and was deeply in debt. Looking for ways to stay afloat, Great Britain decided to try and take more money from the Colonies, despite the fact that the Colonies were doing everything on their own, had their own legislatures and were not even directly represented in Parliament.
Initially, the Colonies were split - some hoped to reconcile, maintaining a strong loyalty to the King and hoping that he would step in and help sort things out, while others saw the benefits of independence. They followed the rules of Parliament for a while and wrote a petition, but support from the King never came. He rejected the petition and Colonial attachment to the Empire was weakened. Movement towards declaring independence became a reality.
Finally, on the 4th of July the Continental Congress adopted the Declaration of Independence, a statement liberating the Colonies from the unjust rule and tyranny of the Empire.
I'm not usually one for big holiday celebrations, but this year I'll celebrate.