It was taxation without representation, meaning that Americans were supposed to pay money to the British government even though they had no representation or ability to give their opinion in that government.
This made the new Americans very angry.
Americans were also angry about the way that the British army treated them.
British soldiers (or people who work in the army) were often quartered (or allowed to live, eat, and sleep in a place for a short period of time) in American homes without the permission (or approval) of the person who owned the home.
Often these soldiers behaved very badly while they were in the home.
This is the second reason why the new Americans decided to begin fighting against the British.
The third reason that Americans fought against the British was because they lacked (or didn't have) self-government, which was the ability to create and run their own government.
The land that would become the United States was far away from Great Britain, yet all the government decisions were being made in Great Britain.
The new Americans longed (or strongly wanted) to make their own decisions, but the British wouldn't let them.
So Americans fought against the British, and this fighting became known as the American Revolution, or the war that ended when the United States became its own country, separate from Great Britain.