What impact does King say that the Emancipation Proclamation had on the American people?

King spoke often about the Emancipation Proclamation. He famously sent a telegram to newly inaugurated President John F. Kennedy in 1961 petitioning the President for a "second Emancipation Proclamation" in the form of federal civil rights legislation. On another occasion, speaking in New York City in a speech commemorating the Proclamation, he cited its importance in establishing justice:

The Emancipation Proclamation shattered in one blow the slave system, undermining the foundations of the economy of the rebellious South; and guaranteed that no slave-holding class, if permitted to exist in defeat, could prepare a new and deadlier war after resuscitation.

While he acknowledged the incomplete nature of the Emancipation--i.e. that it did not actually bring about an end to slavery in regions under federal control, and it failed to bring about any other rights for African-Americans--it began a process by which slavery could be destroyed, and ensured that slavery would end with the destruction of the Confederacy. 
King also referred to the Emancipation Proclamation in his famous "I Have a Dream Speech," where he opened by invoking the memory of the document, issued of course by Abraham Lincoln, whose monument overlooked the proceedings. King said the Proclamation was a "great beacon of light" for millions of enslaved people. But in this speech, as he did in many other mentions of the Emancipation Proclamation, King emphasized the limitations of the freedoms it conferred on Black Americans:

But one hundred years later, the Negro still is not free. One hundred years later, the life of the Negro is still sadly crippled by the manacles of segregation and the chains of discrimination. One hundred years later, the Negro lives on a lonely island of poverty in the midst of a vast ocean of material prosperity. One hundred years later, the Negro is still languishing in the corners of American society and finds himself an exile in his own land. So we have come here today to dramatize a shameful condition.

Like the Declaration of Independence, the US Constitution, and other sources of American liberties, the Emancipation Proclamation was a promissory note to the American people, one which had yet to be called in. King framed the Civil Rights Movement as an attempt to make good on that promise.