In the Bible, Christ raises Lazarus from the dead. Christ teaches us that physical death is not the end of life. Whereas sickness, death, and earthly suffering may seem awful to non-Christians, to Christians they are but temporary inconveniences on the way to salvation and eternal life. Christians, however, must face a deeper fear than the fear of death: they may fear that their faith is not sufficient to bring them eternal life. This deeper fear is the true "sickness unto death."
The Introduction expands on the themes of the Preface, offering some suggestion of what Kierkegaard means by "despair," as well as some explanation of how Kierkegaard interprets Christ's teaching of the resurrection. Christians are aware of the teaching of eternal life. According to Kierkegaard, this knowledge frees them from the earthly cares and concerns that afflict non-Christians. However, just as it makes them aware of the possibility of eternal happiness, so does it also create the possibility of a deeper unhappiness or despair: they may worry that their faith in God is not strong enough to bring them eternal life.
This relationship between Christianity and despair is a good example of dialectics. Kierkegaard implies that there is a dialectical balance between happiness and unhappiness. The pagan or non-Christian enjoys earthly pleasures that are balanced by the earthly fear of sickness and death. The Christian enjoys higher spiritual pleasures, including anticipation of eternal life. But these higher pleasures bring about a higher fear: the fear that one will suffer an eternal death and not enjoy eternal pleasures.