in what way is the concept of 'no taxation without representation' central to america's identity as a nation

Taxation without representation means that the government is asking people to pay the taxes, but isn't providing them with representatives who will fight for them. This is what happened in America while it was still a British colony - Britain 'ruled' over America, taking its taxes, but Americans didn't have a representative in the government who will defend them. This was one of the causes of the American revolution against the kingdom.

The concept of 'no taxation without representation' is central to America's identity as a nation because of the aforementioned. Due to its history with Britain, America fought not to be ruled by any other nation ever again. Its taxes will be only its own and there will be no one else to take the fruits of their labor.