Bigger is a young man dominated by fear living in a world of limited aspirations, but nevertheless it is a world he cannot fully understand. His murder of the white woman Mary is accidental, and it is born of his terror that she will accuse him of rape. His motive is not to kill her but to keep her quiet: he is not thinking clearly when he suffocates her.
Bigger kills his black, alcoholic girlfriend Bessie in a violent way because he fears she knows too much about his murder of Mary. This crime again reveals Bigger's intense fear of the world and limited understanding of how to best deal with his situation, both of which dehumanize him.
Bigger suffers arrest, trial, conviction, and execution for the accidental killing of Mary, but experiences no consequences for killing Bessie even though that crime was deliberate. Bessie's death does not matter except in the sense that it helps support the case against Bigger for murdering a white woman.
The novel is a cry for social justice, showing that the severe limitations put on black people and the fear they live with leads to crime, violence, and death.