i.e. Mississipi (37.45%), Louisiana (31.95%), Georgia (30.88%), South Carolina (27.00%), Alabama (26.42%)
Source: http://worldpopulationreview.com/states/black-population-by-state/
Briefly, this is due to those states' historic connection to black slavery. First, Southern states were economically (and in many ways culturally) reliant on African-American slavery. Second, those states went on to form the Confederacy specifically to protect against what they feared was a threat to the institution of slavery.
Dating back to the colonial period, black slavery existed in both northern and southern colonies but it was generally a stronger presence in the south. The southern economy became dependent on unfree labor to produce cash crops, often though not exclusively on sizable plantations (these varied regionally, but the biggest one early on was tobacco). Meanwhile, northern colonies were originally more oriented toward family farms and, toward the end of the colonial period, a more diverse commercial economy. While there were enslaved African-Americans in both north and south, the southern colonies were much more economically reliant upon them and imported many more of them from abroad.
In the first half of the nineteenth century, these trends intensified. For complex reasons, Northern states one by one started to abolish slavery. But Southern states essentially doubled down on an economy powered by African-American slavery. This trend in the South was strengthened by two additional factors: the invention of the cotton gin, which made cotton production much more profitable in large portions of the South where it had not been profitable before, and the expansion of the U.S. into what is now known as the "Deep South"--states like Mississippi, Alabama, etc. which had rich soil for growing cotton. These Deep South states became the centers of cotton production and (as the transatlantic slave trade had been banned by Congress in 1808) came to import enslaved black people from the "Upper South"--states like Virginia where plantation agriculture was becoming less profitable due to soil exhaustion. On the eve of the Civil War, the vast majority of African-Americans were both enslaved and living in the South.
The Southern states that formed the Confederacy seceded from the United States to protect the institution of slavery. For a long time prior to the Civil War, Northerners and Southerners had clashed over the issue of slavery. It got especially hot in the 15 years or so prior to the Civil War, as the issue of whether new western states being admitted to the Union would permit slavery or not arose following the Mexican-American War. Though there were some Northerners who opposed slavery on moral grounds, most opposition to slavery resulted from distrust of something called the "Slave Power;" Northerners argued that slaveholders had warped the institutions of the federal government and bent them to their advantage. As such, by the time of the election of Lincoln in 1860, Northerners were less immediately interested in complete abolition of slavery, and were more interested in limiting its power over the federal government and its expansion into new territories. There is significant evidence that slavery was not ebbing away, but actually expanding into places further west (such as Texas), and threatening to expand in other places (such as Kansas)—something that really concerned Northerners, mostly because it would enhance the political power of slaveholders. At the time of his election, limiting—but not immediately abolishing—slavery and its power was the position of Lincoln and most of the Republican Party.
White Southerners, however, interpreted Lincoln's election as a direct threat to the long-term survival of slavery, and seceded to maintain their power and protect the institution of slavery—the foundation of their economy, and even for poor white Southerners who did not own slaves, a cultural system that made them feel racially superior to others. Some worried that Lincoln would try to abolish slavery directly, whereas others worried that admitting new free states would lead to the eventual demise of slavery due to a numerical disadvantage for slaveholding states in Congress. Slaveholding states and Confederate leaders specifically declared protecting the institution of African-American slavery as their motivation for seceding.
For a good primer on this history, check out the first few chapters of James McPherson’s book Battle Cry of Freedom: The Civil War Era, as well as the first bit of Bruce Levine’s book The Fall of the House of Dixie: The Civil War and the Social Revolution that Transformed the South. Feel free to let me know if you have any follow-up questions, happy to help clarify!