Why were The Colonies so valuable to Great Britain?

Depends on which colonies. The Thirteen Colonies in North America provided a valuable source of raw materiel, which colonial merchants/companies sold to British merchants, which allowed Great Britain to compete as a trading power. Additionally, the raw materiel provided by the colonies towards Britain was a boon to Great Britain's ability to make war (vis a vis requisitioning these resources in times of crisis), and was a general aid to the British economy. Furthermore, the social and political thought of the times made the colonies (particularly the American colonies) a prestigious possession that brought honor and legitimacy to the British crown, and the British parliament. Ultimately, however, Britain would acquire far more practical, and far more valuable colonies in the course of the 19th century.