Martin Luther King, Jr. gave his well-known "I Have a Dream" speech in 1963 during the March on Washington for Jobs and Freedom. President Kennedy had proposed a Civil Rights Bill in Congress and the march was to support that effort.
At this time in history, African Americans had few rights, particularly in the southern portion of the United States. They had the technical right to vote, but racists did everything possible to keep them from voting, including murder. They had the technical right to "life, liberty, and the pursuit of happiness," but the Ku Klux Klan tried to keep people in a state of terror. Outside of these technical rights, African Americans were not allowed to attend the same schools, eat in the same area of restaurants, use the same restrooms, or even drink out of the same water fountains as white people. It was difficult for them to get jobs that weren't for menial labor.
The yearning for freedom was strong in the hundredth anniversary of the Emancipation Proclamation. Lincoln had freed enslaved people on January 1, 1863, but these people were still not truly free.
King's purpose in giving the speech, then, was to mark the hundredth anniversary of the Emancipation proclamation by showing the majesty of American rhetoric from the great texts that influenced the development of this country (the Constitution, Declaration of Independence, and even patriotic songs such as "My Country Tis of Thee") and comparing that to African American's everyday lives. He then tells of his dream that things will change, so he provides hope for the future.