We celebrate American Independence Day on the Fourth of July every year. We think of July 4, 1776, as a day that represents the Declaration of Independence and the birth of the United States of America as an independent nation.
On July 4th, the Continental Congress formally adopted the Declaration of Independence, which had been written largely by Jefferson. Though the vote for actual independence took place on July 2nd, from then on the 4th became the day that was celebrated as the birth of American independence.