David Walker's Appeal to the Colored Citizens of the World is actually arranged into four articles or essays; looking at each one individually is a good way to answer this question. The first is entitled "Our Wretchedness in Consequence of Slavery," and in it Walker observes that African Americans suffered a worse form of slavery than even the Israelites in the Old Testament, the helots in ancient Sparta, and other historical examples. This is not only because of the brutality of the institution, but because of its racial underpinnings. Not only are enslaved men and women denied their freedom, but their humanity itself is denied by the racism of a slave society. African Americans (and not just slaves) are told "because we are helpless, that we are not of the human family."

The second article, "Our Wretchedness in Consequence of Ignorance," takes up a similar theme. Walker writes that

[i]gnorance and treachery one against the other—a groveling servile and abject submission to the lash of tyrants, we see plainly,my brethren, are not the natural elements of the blacks.

He points out that enslaved people have been kept in a state of ignorance by their oppressors, who then cite that very ignorance as a reason for their enslavement in the first place.

The third article, "Our Wretchedness in Consequence of the Preachers of the Religion of Jesus Christ," observes that the Christianity professed by slaveowners is hypocritical and wicked because they actually use it to oppress enslaved people. "Can any thing," he asks, "be a greater mockery of religion than the way in which it is conducted by the Americans?"

Finally, in "Our Wretchedness in Consequence of the Colonizing Plan," Walker makes a fourth point. He characterizes the so-called "colonization" movement advocated by many prominent Americans, as fundamentally wrong-headed. Taking aim at Henry Clay, the most prominent advocate of "colonizing" blacks to West Africa, he argues that colonization is a way for whites to wash their hands of the sin of slavery without consequence. In this chapter he reaches a crescendo, arguing that enslaved people would one day rise up to overthrown their masters and destroy the institution. So these four chapters make interrelated points: slavery denied the humanity of blacks; it rendered them ignorant; it was fundamentally contrary to Christian teaching; it was bound to end in violence and turmoil unless right-thinking people ended it.

Essentially, Walker's Appeal can be seen as identifying four elements that build its argument.  These points would involve Walker's treatment of "Slavery," "Ignorance," "the Preachers of the Religion of Jesus Christ," and "the Colonizing Plan."  In detailing the condition of "Slavery," Walker's main point is that the historical advancement of societies that have included slaves have been some of the most cruel and brutal known to the historical tradition.  Yet, Walker makes clear that even in these settings, slaves were able to find some sanctuary in being part of a "human family."  Walker's point is that the slavery seen in America is fundamentally different than any other previous time because it prevents the person of color from participating in this notion of "human family."  

Walker than engages in a study of how American slavery has been carried out to prevent people of color from participating in American society.  His discussion of political initiatives such as the Three- Fifths Compromise, or codes that limit education to people of color, as well as social marginalization that is reinforced through violence and repression are examples of how "ignorance" has become so much a part of the landscape. Walker wants his “afflicted and slumbering brethren” to arise out of this condition and take action.  From here, Walker criticizes the use of religion as a way to keep slaves in submission and to even justify slavery.  An ordained minister himself, Walker understands how religion has been used in a hypocritical manner and thus seeks to offer clarification as to how religion has been twisted. His criticism of "the Colonizing Plan" is a point that he wishes to emphasize.  Walker does believe that there can be an America with people of color in it.  The re-colonization of African- Americans is something that Walker himself cannot get behind and support because it removes people of color from their rightful place in America. In these four point, Walker's analysis lies in his Appeal.