On 4 July 1776 the Founding Fathers gathered in Philadelphia and put their quills to the Declaration of Independence, which is why America fireworks itself silly every 4 July. The famous painting shows them all there, signing the great document on the great day.
The 4th is the day Congress approved the wording of the Declaration, not the day it was signed. The signing mostly happened on 2 August 1776, when an engrossed copy on parchment was ready and delegates added their names over time, with some signing even later. John Adams actually thought the 2nd of July, the day Congress voted for independence, would be the date Americans celebrated. The 'all signed together on the 4th' image owes a lot to John Trumbull's grand painting, which compresses events for drama. So the holiday marks the adoption of the text, which is a fine thing to mark, just not the mass quill-dipping everyone pictures. The most famous signature, John Hancock's, did go on around the 4th as president of Congress. The other fifty-five trickled in.