What did Martin Luther King Jr. mean when he said, "Freedom was never voluntarily given by the oppressor"?

King means that those who are in control, never voluntarily give up that control.  Whether you consider the English in India, ante-bellum plantation owners in the American South, or whites in apartheid South Africa, those in control do not willingly give up their power.

By implication, King applies this to civil-rights era America.  "White" America will not voluntarily give civil rights to "black" America.  They will have to in some way be made to give blacks civil rights.