After Columbus "discovered" the Americas, people started making their way to this New World, including many citizens of England (like the Jamestown Settlement in 1607 and the Mayflower's arrival in 1620). The colonization of the New World progressed fairly rapidly over the next 150 years considering the only form of crossing the Atlantic Ocean was by slow-moving boat. But as these colonies formed, they were still governed by the British. It was the Colonists' unhappiness with the British government that led to the The Declaration of Independence
The Colonies considered the ruling of the British — specifically King George III — to be tyrannical and unfair. The Declaration of Independence addressed the Colonists issues with comments like "He has kept among us, in times of peace, Standing Armies without the Consent of our legislatures" (which likely lead to the 3rd Amendment in the U.S. Constitution). The signers of the Declaration also bluntly pointed out, "He has plundered our seas, ravaged our Coasts, burnt our towns, and destroyed the lives of our people."
The Declaration of Independence was no love letter to the King of England, it was a statement informing the king that he was being "fired" Donald Trump-style. This was the official statement by the Colonies to the British government that they would no longer recognize British rule, and was a statement to fellow Colonists that it was time for the Colonies to be governed by Colonists. Of course the British were unwilling to walk away without a fight, so the Declaration of Independence eventually led to the American Revolutionary War.
Signed on July 4, 1776, the Declaration of Independence is considered the birthday of our nation. It helped shape some of the amendments of our Constitution revered because without it, the United States of America may not have ever come to exist.