There is a hierarchy of forms of despair: the more conscious one is of one's despair, the more intense the despair is. Section (a) of Part I.C.b. describes ignorant despair. Section (b) describes two forms of conscious despair: "weak" despair and "defiance."
Ignorant despair is the despair of not knowing that one is in despair. This is the most common form of despair. It is the natural state of all pagans (non- Christians) and others who fail to concern themselves with spiritual matters. Such people are naturally defensive when they are told that they are in despair. Nevertheless, it may be easier for them to overcome despair than it is for people with a deeper awareness of their despair.
Section (b) explains that consciousness of despair varies according both to how aware one is of one's own despair and to how aware one is of what it means to be in despair. Pagans, for instance, may feel that they are in despair, but they cannot be fully conscious of the depth of their despair, since they are not aware of Christian teachings of salvation.
Subsection alpha describes "despair in weakness," alternatively defined as the despair of "not wanting to be oneself." In this form of despair, individuals lose the desire to be who they are. These individuals fall into two categories. First, there are those who are focused on earthly events and circumstances and fall into despair because of some aspect of their earthly lives. These people don't want to be themselves because they wish their lives had turned out differently. Second, there are those who are aware of spiritual possibilities but refuse to pursue them. These people are more conscious of themselves and of despair. They don't wish to be themselves because they feel unwilling or unable to focus on spiritual matters, even though they know that it is weak to be focused on earthly events.
Subsection beta describes the despair of "defiance," alternatively defined as the despair of "wanting to be oneself." In this form of despair, the individual wishes to be the complete master of his or her destiny (which of course is impossible). This form of despair is "demonic."
The distinctions Kierkegaard draws in this section are often confusing and unclear. If you feel as if Kierkegaard has completely lost you, it may be helpful to remember that some experts have interpreted The Sickness Unto Death as a parody of philosophical books that draw too many distinctions and categorizations. (See the commentary to Part I.A.).
As with Part I.C.a., it may be most useful to focus on the examples Part I.C.b. gives of what Kierkegaard means by "despair." In this section, we learn that people automatically suffer despair when they are unaware of despair. We learn that despair becomes more intense when people are more aware of it. We are given examples of people falling into despair over negative events in their lives, of people living in despair because they lack the strength to lead spiritual lives, and lastly of demons and stoics who live in despair because they refuse to be dependent on anything, even God. We are told that these examples of despair form a hierarchy running from the least conscious (and therefore most innocent) to the most conscious and most intense.
Again as in Part I.C.a., the general point of all these examples is that despair involves a failure to be a human being in the fullest sense. People who focus too much on earthly concerns neglect their spiritual side. Defiant people exaggerate their capacity to control their destiny. All of the people Kierkegaard describes in this section have neglected some aspect of themselves.
Several passages Part I.C.b. merit particular attention. Take note of the second paragraph of section (a), which comments on thinkers who study "world history" and erect complex philosophical "systems." Kierkegaard is often assumed to be talking about Hegel here, but his comments can be understood as a concise statement of his disagreements with those who practice "science" and "scholarly" writing. Such people go about their lives investigating the material world or studying history. They may have great insights, but they neglect the fact that knowledge about the world is irrelevant to personal salvation. Kierkegaard disapproves of this approach to life because he sees personal salvation as the fundamental task of all human beings.
Also noteworthy are Kierkegaard's sarcastic comments about organized religion. In subsection alpha of section (b) he pokes fun at people who are Christian in the same sense that someone from Holland is Dutch. He also comments approvingly on people who don't go to church because they think pastors don't know much. Kierkegaard is famous for arguing that being a Christian involves an intense personal commitment. In this and other works, he frequently makes fun of people who adopt a more casual approach to religion--thinking, for instance, that attending church once a week is enough to make them Christian.
Lastly, note that Kierkegaard writes repeatedly of "dialectical" relationships between forms of despair. Also see the commentary to the Preface for explanation of this term.