The District constituting the seat of Government of the United States shall appoint in such manner as Congress may direct:
A number of electors of President and Vice President equal to the whole number of Senators and Representatives in Congress to which the District would be entitled if it were a State, but in no event more than the least populous State; they shall be in addition to those appointed by the States, but they shall be considered, for the purposes of the election of President and Vice President, to be electors appointed by a State; and they shall meet in the District and perform such duties as provided by the twelfth article of amendment.
The Congress shall have power to enforce this article by appropriate legislation.
This amendment allows the District of Columbia (Washington, DC) to have delegates in the electoral college when it comes to presidential elections. It does not change anything else about the way DC is govern, which even today is debated. It is not a state, but a territoty. It is governed by Congress, and has no representation that can vote within congress (It does have 1 unvoting representative in the House).
Currently DC has 3 electoral votes.
This was passed by Congress in 1960, and ratified in 1961.