This book is undeniably Christian philosophy, although Kierkegaard writes extensively (in other books) about his own issues with religion (he has many issues with standard, cookie-cutter Christians). However, without at least understanding the religious experience he describes, at least hypothetically, it will be impossible to understand his words.
That's a difficult challenge, because it involves the act of trusting that God is in control of each of our individual realities. Not only that, Kierkegaard describes faith to be the kind of thing where only the faithful see the benefits of faith in their lives. It's as if what is most important in life is only discoverable when one commits their self toward whatever their fate is.
Typically, fate is a kind of sacrifice, at least in this book. The title of the book is also Biblical by the way. It's a blatant allusion to a verse in Paul's epistles where Paul urges the followers of Christ to "Work out your salvation with fear and trembling." The value of this title is that it shows that Kierkegaard believes that to sacrifice one's will to serve their fate is the same idea as "working out your salvation."
In other words, Kierkegaard is trying to borrow something essential from Christianity and give a more academic, philosophical defense, although his philosophy is thoroughly informed by his own religious beliefs, so ultimately, the reader will need to draw their own conclusions about such things as fate, destiny, or God.
