I think shmoop has the best take on the novel's narration;
The Book Thief Narrator:
Who is the narrator, can she or he read minds, and, more importantly, can we trust her or him?
First Person (Limited)
The Book Thief is narrated by an extremely overworked being who identifies himself as Death. Some readers love Death as a narrator; others not so much. We tend to think it's an interesting choice. Markus Zusak needed a narrator who could provide Liesel's point of view, but also provide information that Liesel, as a young girl in a relatively isolated town, wouldn't know about. He needed a narrator who could provide snapshots of the World War II outside of Himmel Street. Zusak could've just used a third-person narrator, but by using Death the author is able to offer a unique perspective on all the death and dying occurring during this historical period.
Now, Death is not omniscient – he doesn't know and see everything that's going on in the world. He's gets his information just like we do – from his personal experiences and from what he reads and hears about from others. In this story, much of what Death relates to us falls into the second category. His chief source for the story he's telling is The Book Thief, the book Liesel writes about her life.
But, for Liesel's story to make sense to us, Death needs to tell us about what's going on in other parts of Germany, Poland, and Russia during World War II, to provide us with details Liesel would have no way of knowing at the time she's writing her book. Dying is one of the main things going on. He interweaves this larger context with the story of Liesel and the people she loves and loses.
Check out Zusak had to say about why he chose Death as the narrator for The Book Thief:
Well, I thought I'm writing a book about war, and there's that old adage that war and death are best friends, but once you start with that idea, then I thought, well, what if it's not quite like that? Then I thought what if death is more like thinking, well, war is like the boss at your shoulder, constantly wanting more, wanting more, wanting more, and then that gave me the idea that Death is weary, he's fatigued, and he's haunted by what he sees humans do to each other because he's on hand for all of our great miseries. (source)
Now what do you think? Was Death a good choice for the role of narrator? What would the book have been like if it was narrated by a third-person narrator? Or by Liesel?