It was the Declaration of Independence that was approved by the Second Continental Congress on this date in 1776.
Independence itself was voted two days earlier. We celebrate the anniversary of the birth certificate, not the birth.
Although the section of the Lee Resolution dealing with independence was not adopted until July 2, Congress appointed on June 10 a committee of five to draft a statement of independence for the colonies. The committee included Thomas Jefferson, John Adams, Benjamin Franklin, Robert R. Livingston, and Roger Sherman, with the actual writing delegated to Jefferson.
Jefferson drafted the statement between June 11 and 28, submitted drafts to Adams and Franklin who made some changes, and then presented the draft to the Congress following the July 2nd adoption of the independence section of the Lee Resolution. The congressional revision process took all of July 3rd and most of July 4th. Finally, in the afternoon of July 4th, the Declaration was adopted.
The signing of the embossed copy we recognize as THE Declaration of Independence began on August 2nd.
Information and quote from The National Archives.