Douglass uses the Fourth of July to bring to light how far America has to go in ensuring that its promises are delivered to all of its citizens.  The mere mention of "Independence Day" rings hollow to Douglass when the same nation condones or refuses to abolish the institution of slavery.  For Douglass, Independence Day offers the best opportunity to explore the chasm between America's promises and its realities.  The promises of freedom for wealthy, white Americans have to be contrasted with the reality of oppression and bondage for its darker skinned inhabitants.  Douglass believes that White Americans have to grasp the fact that as slavery exists, American political hopes ring hollow and its foundational beliefs have to be questioned.

I believe that what you are referring to is the speech that Douglass gave on the Fourth of July in 1852 in Rochester, New York.

In this speech, he is contrasting the meaning of the day for blacks and whites.  Basically, he says that white people should celebrate the day.  To them, it should mean independence and joy.

He says that, for whites, it is a day of celebrating the

rich inheritance of justice, liberty, prosperity, and independence

that white people got from the founding fathers.

Douglass says that whites should greet the day with joy because it is a day of life and healing for them, even if it is not a day that has brought any joy to blacks.