After slavery became a significant part of Colonial American culture and economy, the southern states -- which had longer growing seasons and could support themselves on summer crops like cotton -- began to import more and more black slaves to work the fields. Even after the Civil War, when slavery was abolished by the Thirteenth Amendment, blacks continued to live and work in the southern states.
Because of the large numbers of slaves needed to work the fields, some of the southern states had populations with a black majority. Louisiana, South Carolina, and Mississippi all had black population exceeding the white population, and since slaves had no freedom to move, they continued to work there. Georgia, Alabama, and Florida had high black slave populations as well, but not a >50% majority. It is important to note that the black majority population had little-to-no effect on the politics, culture, or society at the time; slaves were not considered real people and so a black majority state was still a white-controlled, white-cultured state.
After Emancipation, free blacks began to move north, where they could work and support their families without the ingrained discrimination, prejudice, and resentment in the southern states. As of today, only four states -- California, Texas, New Mexico, and Hawaii -- have non-white majority populations.