In giving freedom to the slave, we assure freedom to the free - honorable alike in that we give and what we preserve. We shall nobly save, or meanly lose, the last best hope of earth.

This quote means that if we give freedom to people who have been enslaved, then we are giving freedom to the people who are already free. Doing this is an honorable thing, because we are both giving freedom and preserving it. We have a chance to save the best hope of earth, but there is a risk that we may fail to do so.