An external tax was one imposed on imports into the American colonies. A prime example of this would be the Sugar Act of 1764, which was imposed by the British to raise much-needed revenue to help them pay for the upkeep of their troops on American soil. This measure proved deeply unpopular and led to widespread civil disturbances throughout the colonies.
An internal tax was one directly levied upon the property and goods of the colonists. A notorious example would be the Stamp Act of 1765, which required that many printed materials in the colonies were to be printed on stamped paper produced in London and needed to have an embossed revenue stamp. Inevitably, this greatly increased the cost of printed documents, which were essential to American trade, law, and the dissemination of ideas in books and pamphlets. If anything, the Stamp Act proved even more unpopular than the Sugar Act, and pushed the American colonists closer to outright resistance to British rule.