Joseph E. Brown was Governor of Georgia from 1857 to 1865. After the election of Abraham Lincoln as President in 1860, Brown, like many of his fellow Southerners, felt that the time had come for the South to secede from the Union. They were convinced that, despite what Lincoln had said on the campaign trail, it was only a matter of time before he abolished slavery, the lynchpin of the Southern economy and society.
The day after Lincoln's first Inauguration, a convention was held in Arkansas to determine that state's position with regards to the issue of secession. By this time, seven Southern states had already seceded from the Union, forming themselves into the Confederacy. One of those states was Georgia, led into secession by Governor Brown. He sent a letter to the Secession Convention, in which he urged Arkansas to join the Confederacy.
In his letter, Brown argues that Lincoln's election spells the end of slavery in the Southern states. Although Lincoln's priority was in holding the Union together, even if it meant retaining slavery, Brown maintains that the Republican Party is dominated by abolitionist sentiment, and that the abolitionists within the Party will be emboldened by Lincoln's election to achieve their long-held ambition.
Brown goes on to say that the abolition of slavery will lead to the impoverishment of those millions of Southern whites who don't own slaves. He doesn't specify exactly what the consequences would be for poor whites, but we can surmise that he's concerned about white workers being undercut by free blacks in the labor market. As a slave-holder himself, Brown also expresses concern at the prospect of people like him being deprived of their "property" without compensation. The consequences of such a policy, he predicts, will be utter ruin.
Brown also predicts—wrongly, as it turns out—that secession will not lead to war, but that submission to the will of the North will. In presenting such a cavalier attitude to the prospect of civil war, Brown is trying to persuade the people of Arkansas that they have nothing to fear from secession, and they should take that fateful leap to protect their rights and the institution of slavery from a hostile federal government in Washington.