Using repetition in a speech is a persuasive device used to not only organize a speech but to give emphasis to a particular idea. It is an effective device to let your audience know the key points of your speech. It is also a persuasive device to appeal to your audience's emotions.
When Martin Luther King, Jr. used the repetition of the line, "I have a dream . . ." he is presenting to his audience an outline of his demands and expectations. Through these repetitions, he is also persuading his audience emotionally by recounting the injustices suffered by blacks, and his dream that some day these injustices will be changed.
Many of the "I have a dream" sections use references or allusions to well-known speeches, the values established by our Constitution, and references to the American dream that has been denied to black Americans.
King's speech is an emotional appeal to the logic and reasoning of those who have denied him the freedom he has sought during the Civil Rights Movement and his life. By appealing to the audience's feelings and emotions, he hopes to convince them to back his cause. The repetition of the lines only adds to the sentiment he wishes to convey. He is also putting into words the dreams that all black Americans were searching for in America.