What does "no taxation without representation" mean?
Much of this had to deal the dissatisfaction of the way the colonists had been treated by the British Gov't. Colonists hoped to be treated as they had been as citizens of Britain. Parliament had taxed colonists unfairly without any representation. Therefore, they found that this was an example of external taxation.
Why did the English colonists not rely on the English Parliament to meet their needs during colonial times?
Much of this had to do with distance and necessity. Britain was very far away. So the colonists needed to fill the void and avoid chaos. They got very good at self governance and flourished under self-rule.