July 4, 1776 is often thought of as the day that the Continental Congress declared independence from Great Britain. In fact, they did this on July 2, 1776. People have also associated July 4 with the day that the Declaration of Independence was written and delivered to Great Britain. In reality, the first draft of the Declaration of Independence was written in June of 1776 and did not arrive in England until November 1776.
July 4, 1776, was actually the day that the wording of the Declaration of Independence was approved by the Continental Congress. Once the final draft was complete, it was signed on August 2, 1776 by most members of Congress.
Though the first July 4 may not have happened exactly as you thought it did, it was nonetheless a seminal day in American history. Happy Independence Day!
For additional reading about July 4 and the American Revolution, see the book list below: