I assume that you are asking about King's famous "I Have a Dream" speech delivered in August of 1963. The main point that King is making in this speech is that he believes that America can live up to its ideals by creating a society in which people of all races are equal.
King starts out by saying that the Declaration of Independence and the Constitution make promises that are not being fulfilled. He says that blacks in America have not had the freedoms that those documents promise. He says that their movement is pushing for those freedoms but that it must do so nonviolently and it must have both whites and blacks working together.
He then goes on to talk about the aims of the movement, about what will satisfy the movement. This is where the most famous parts of the speech come in. He says that he will only be satisfied when his dream is fulfilled and there is equality. He will only be satisfied, for example,
when all of God's children, black men and white men, Jews and Gentiles, Protestants and Catholics, will be able to join hands and sing in the words of the old Negro spiritual:
Free at last! Free at last!
Thank God Almighty, we are free at last!