In his famous and frequently quoted "I Have a Dream" speech, Dr. Martin Luther King Jr. makes his view of the "American Dream" clear. To him, the American dream is one of equality for all people. The Oxford English Dictionary defines the word equality as "the state of being equal, especially in status, rights, and opportunities."

By equality, Dr. King means that all citizens—including both black citizens and white citizens—are treated justly. For Dr. King, the American dream is a dream of justice. It is a dream of equal, fair, and equitable treatment for all peoples living in the US. It is also a dream of peaceful coexistence, and it is important to remember that, despite the number of people gathered in protest and the simmering racial tensions in the country (particularly in the south), the marchers demonstrated peacefully. In his speech, he refers to "the state of Mississippi" as "a state sweltering with the heat of injustice, sweltering with the heat of oppression." His dream is that it "will be transformed into an oasis of freedom and justice."

This speech was given at the historic March on Washington. An estimated 250,000 protesters had assembled in front of the iconic Lincoln Memorial in Washington, D.C. Their choice of location was intentional, as the march came some one hundred years after President Lincoln signed the Emancipation Proclamation granting freedom to American slaves. Their goal was to protest the unfair treatment and continuing challenges and inequalities that African Americans faced on a daily basis, even a century after Lincoln’s action. Their objective was to make the nation take notice.

In his moving “I Have a Dream” speech, Martin Luther King Jr. begins by referencing Lincoln's Gettsyburg Address. He says,

Five score years ago a great American in whose symbolic shadow we stand today signed the Emancipation Proclamation. This momentous cleared is a great beacon light of hope to millions of Negro slaves who had been seared in the flames of withering injustice… But 100 years later the Negro still is not free.

The beginning of Dr. King’s speech parallels Lincoln’s Gettysburg Address, which started with “Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal.” In this use of parallel text, Dr. King drives home his hope for equality and emphasizes the fact that “all men” are created equal.

The “I Have a Dream" speech was to be the declaration of Dr. King’s Southern Christian Leadership Conference (SCLC) and African Americans across the US that injustice will not stand. He says, “There will be neither rest nor tranquility in America until the Negro is granted his citizenship rights.” He outlines his dream, or his view of the American dream:

I still have a dream. It is a dream deeply rooted in the American dream. I have a dream that one day this nation will rise up, live out the true meaning of its creed: "We hold these truths to be self-evident, that all men are created equal."

The American Dream is that anyone from any walk of life can make it big and find happiness so long as they work hard. This dream assumes that society allows people to achieve this success, regardless of class, race, gender, or any other such demographic classification.

Martin Luther King Jr. believed in the American Dream (he even says his specific dream is embedded within the American Dream itself), but he also knew that it was not a reality for everyone, especially black Americans. Even after slavery was abolished in the United States, black Americans were still repeatedly denied human rights and opportunities that white Americans enjoyed.

In the "I Have a Dream" speech, King believes that the American Dream can only become a reality when all people in the United States view one another as brothers and equals, regardless of racial differences. In this way, King does not deny the validity of the ideals behind the American Dream; however, he does criticize the United States's inability to follow those ideals to their logical conclusion by offering black Americans the same opportunities.

King sees a direct connection between his dream of racial equality and the American dream. He argues that the assertion from the Declaration of Independance that "all men are created equal" is the "true meaning" of the American dream. King goes on to describe his dream, imagining black and white people in Georgia, Mississippi and Alabama living in harmony.

It's clear that King embraces the ideals of the American Dream, but feels that American society has not lived up to this dream as far as black people are concerned. His rhetoric contextualizes the American Dream; by including in it his dream of black and white people sitting "down together at the table of brotherhood" he is, in effect, laying claim to the principle of equality and pointing out the hypocrisy of those that would keep the races unequal. His conclusion of this section of the speech, in which he invokes the Bible ("I have a dream that every valley shall be exalted...") transforms the American dream into a vision of the Kingdom of God. This move explicitly connects the American dream to Christian ideals, but more significantly, suggests that racial equality is less a matter of American politics than it is a kind of divine imperative.

Martin Luther King Jr.'s dream was for all people to be free and treated equally. In August 1963, King delivered his famous speech in which he called upon America to do what it promised. The promise, according to the Constitution and the Declaration of Independence, was that all men would be treated equally. King said, "In a sense we've come to our nation's capital to cash a check." Since this promise had not yet been fulfilled, he stated that the check was marked as having "insufficient funds."

While King was criticized by some for his tone, he hoped that his dream of freedom and equality could be achieved peacefully. He stated, "In the process of gaining our rightful place, we must not be guilty of wrongful deeds." King recognized the "marvelous new militancy" of the community, but cautioned that the America he dreamed of could be achieved by African Americans and whites working together.

The phrase "American dream" can be used in a variety of contexts.  King is clearly using it to mean racial equality.  He is saying that a country and society without discrimination or prejudice would fulfill the American dream.

King does not actually say "the American dream is..."  Instead, he says 

... I still have a dream. It is a dream deeply rooted in the American dream.

He then goes on to tell what his dream is.  It is his famous dream of a country in which there is racial harmony and equality.  It is a country where people are not

judged by the color of their skin but by the content of their character.

King's dream is a dream of racial harmony.  Since he says that it is rooted in the American dream, we can infer that the American dream is also one of harmony and equality.