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.
Section 2. The Congress shall have power to enforce this article by appropriate legislation.
The Twenty-Third Amendment amended Article 2, Section 2 of the Constitution. It gave the District of Columbia electors. It also gave Congress the authority to enforce the amendment through legislation.
The following picture shows what life was like in Washington D.C. before the Twenty-Third Amendment. http://www.livinginaperfectworld.com/wp-content/uploads/2010/10/23rd-amendment.jpg
Although the 23rd Amendment gave D.C. the right to vote for President and Vice President, it did not give D.C. represenation in Congress. This video is fighting for D.C.'s right to representation in Congress.