You already know:
1. Washington, D.C. is the capital of the United States of America.
2. An echo = when a sound is repeated.
So Americans often refer to "Washington's echo chamber."
That is, the politicians, journalists, professors, etc, who live in the capital repeat the same things to one another because most of them read the same newspapers, look at the same TV news shows, attend the same parties, etc.
So if one newspaper says that most Americans prefer vanilla ice cream, then maybe a TV news program will repeat that news, and then maybe a politician will repeat that news, etc.
Maybe the American people actually prefer strawberry ice cream, but the important people in Washington, D. C. do not know that because they do not go out into the country and ask the American people. They only listen to one another repeat (echo) the story that vanilla is the preferred flavor.