The colonists had problems with taxation without representation is because they had no say in the matter. They would pay the taxes but Europe made the decisions with the money. Not any of the colonists could make the Decision of we need new roads, schools, etc.
It was a phrase used to justify European Imperialism in the 19th and early 20th centuries. The phrase implies that imperialism was motivated by a high-minded desire of whites to uplift people of color.