Why was taxation without representation a meaningful slogan? ?

Because the english Americans who came over to live in the colonies didn't have representation in parliament, and after the american-indian war which Britain helped with, made Britain especially in debt (remember they were even fighting with France too), they couldn't look to tax their people too much so they turned to taxing their people in the americas. Eventually after americans won the war against Britain, they needed assurities that the government wouldn't be too powerful like that again.