In chapter 1 of The Souls of Black Folk, Du Bois makes this statement in the context of talking about the disappointment of black people in the United States over what has happened in the forty years since the slaves were freed.
Black people, Du Bois says, long for freedom, but while they are no longer enslaved, neither are they yet entirely free. When he states that the nation has not found peace from its sins, he means that racism still exists and black people are still oppressed. He calls himself, as a black man, an "outcast and a stranger in his own house." Black people, he says, are still a despised group because whites are unable to get over the sin of hating them and thinking them inferior.
"The freedman" who has not yet attained freedom in the "promised land"—the United States—is the black individual who is still terrorized by the Ku Klux Klan and denied his political rights. The poverty, ignorance, and oppression of most black people have a corroding effect on their souls, and this, Du Bois says, must be resisted by struggling for full equality.