About half way through his famous speech, Martin Luther King Jr. declares that "we must take the pledge that we shall always march ahead," and never "turn back." He subsequently says, "We can never be satisfied as long as the Negro is the victim of the unspeakable horrors of police brutality." He was speaking here directly to a crowd of approximately 250,000 people in Washington DC, but the collective "we" is more broadly a reference to all Americans. The speech took place in 1963, in the midst of the civil rights movement in America. This was a movement campaigning for equal rights for African Americans.
The pledge, or promise, that he insisted must be made was the pledge to never stop fighting and campaigning for equal rights despite how difficult and dangerous that fight might become. Indeed, the police brutality he references was a very real danger for those participating in the civil rights movement and must have, inevitably, made some campaigners think twice about continuing the fight for equal rights. Just two years later, in 1965, media coverage of police brutality aimed at the demonstrators who marched from Selma to Montgomery caused widespread outrage and widespread sympathy for the civil rights movement.
In the same part of the 1963 speech, King repeatedly says that "we can never be satisfied" and then follows this with a series of conditions, such as "as long as our children are stripped of their selfhood" and "as long as a Negro in Mississippi cannot vote." Finally, at the end of this section of the speech, King declares that "we will not be satisfied until justice rolls down like waters and righteousness like a mighty stream." In other words, King implies that African Americans specifically, and all Americans more broadly, will only be satisfied when African Americans are no longer persecuted and oppressed and when there is "justice" and equality for all men regardless of their color or race.