The idea of "no taxation without representation" is pretty simple. It means that people should not have to pay taxes to a government if they do not get to help decide how that government is run. Usually, this means people get to vote for someone to represent them.
This idea became well-known during the American Revolution. At that time, people who lived in the colonies were upset because Great Britain was making them pay taxes without letting them have a say in the British government. The American colonists wanted to be treated and have some control over what happened to them. They wanted rights, and the phrase "no taxation without representation" was a way to express these demands. The American colonists used this phrase to make it clear that they believed "no taxation without representation" was a right.