He's essentially saying that freedom has to be fought for. It will be not be given to us by those in power and authority; we need to take it for ourselves. Yes, as human beings we're all free and the Constitution says we're all equal, but out in the real world we need to struggle in order to gain and secure our civic freedoms. This is King's general message, one that has universal application to all of us, irrespective of race.
However, more importantly, his message also has more specific application. King is encouraging African Americans to keep on with the civil rights struggle, and not to lose hope. He understands the importance of freedom from a theoretical perspective but he knows that freedom's true significance lies in its practical application. Formal, legalistic freedom has not guaranteed civil rights to African Americans; only substantive freedom, gained through long and painful struggle, will suffice.