Actually, part of my explanation wasn't fully correct:

Independence Was Not Declared on July Fourth: The second Continental Congress actually voted for independence on July 2. In fact, John Adams wrote to his wife, Abigail, predicting that future generations would celebrate July 2 as Independence Day, saying, "The second day of July, 1776, will be celebrated by succeeding generations as the great anniversary festival. It ought to be solemnized with pomp and parade, with shows, games, sports, guns, bells, bonfires, and illumination, from one end of this continent to the other, from this time forward forevermore." July 4, 1776 is significant because that is the day that Congress officially adopted the Declaration of Independence document, but contrary to what many people believe it was not signed on the July 4. The official signing ceremony occurred on August 2, which is when most of the signers affixed their names to the document, but other representatives signed the document throughout the summer of 1776. Finally, there is no historical record of John Hancock saying that his signature is that big so that King George could read it. It has been suggested that Hancock's is by far the largest signature simply because he was the president of Congress.