Britain had just gone bankrupt due to expenses in fighting what Winston Churchill called the first world war, (French & Indian War in the North American theater) To recoup, to make money, Britain imposed taxes on its colonies. The American colonies were split. 1/3 of American colonialists supported a war of independence. 1/3 were Loyalists, 1/3 were neutral or didn't care. But the American rebels dominated and the rebellion began with the Declaration of Independence in 1776. Britain wen to war to keep the American colonies.
"The colonialists" is ambiguous, as it could include the Canadian colonies, which stayed loyal to Britain. The 13 states were the first British colonies to escape from the British Empire. But Britain didn't give up entirely after losing, they came back again in 1812, with the War of 1812, which has been called America's 2nd war for Independence.