Washington is a proper noun, referring to the U.S. capital city, Washington, D.C. It is used to refer to the city, its people, the state of the same name, or any other entities associated with the city or state.
Washington is always capitalized when it is used as a proper noun. When using the word to refer to the city or state, it should always be accompanied by the noun it modifies (e.g., Washington D.C.; Washington State).
1. She was born in Washington D.C.
2. The Washington State Legislature meets annually.
3. His trip to Washington included a guided tour of the Capitol.