Colonial America refers to the period of American history (roughly late 15th century to the mid-19th century) when European states exercised political control over indigenous Americans and European settlers in the Americas. Colonial powers in the Americas included the Spanish, British, French, Portuguese, Dutch, Swedes, and Russians. The term is sometimes taken to refer to pre-Revolution British colonies that would eventually become the United States.
The period covered by this term varies with the particular history of the colony in question. For example, Spanish Colonial America lasted from the late 15th century into the early 19th century.
The most common association with the term, however, is with the history of those British colonies that would become the United States. "Colonial America" would then be taken to refer to the period from the first British settlements in Virginia and Massachusetts in the early 17th century until the Declaration of Independence in 1776.
While the British maintained colonial possessions in the Americas long past 1776--for example, they had possessions in Oregon, Canada, and the Caribbean--colonialism in American declined steadily throughout the 19th century.