The narrator in The Unbearable Lightness of Being is probably one of the most unique narrative voices in 20th century literature. The narrator refers to himself in the third person, initially suggesting that he is a character, if a peripheral one, in the story. But he soon confesses to be the author, not the spectator, of the fictional tales. He then proceeds to comment on the characters – his own fictional creations – and analyze his own novel for us.
The first question that comes up is whether the narrative voice belongs to some fictional narrator created by Kundera, or whether Kundera intends the narrative voice as his own authorial commentary. The answer is that we can't be sure either way. This is not cause for concern; you could argue that it doesn't matter to our reading of the novel. This is a particularly apt discussion in light of the narrator/author's claim that real lives are composed much like fiction – with symbols, symmetries, and recurring motifs that are arranged with an eye for beauty. Check out "Symbolism, Imagery, Allegory" for a full discussion of this concept. The point the narrator makes here is that his characters are no less "real" for the "fictional" elements that fill their lives. Fiction is supposed to mirror life, but life also mirrors the artistry of fiction because of our innate aesthetic sense.
The narrator becomes more directly involved in the novel in Part 5, Chapter 15, when he directly discusses his own relationship to the characters. It's a long passage, but worth a close read (or six):
As I have pointed out before, characters are not born like people, of woman; they are born of a situation, a sentence, a metaphor containing in a nutshell a basic human possibility that the author thinks no one else has discovered or said something essential about. But isn't it true that an author can write only about himself? Staring impotently across a courtyard, at a loss for what to do; hearing the pertinacious rumbling of one's own stomach during a moment of love; betraying, yet lacking the will to abandon the glamorous path of betrayal; raising one's fist with the crowds in the Grand March; displaying one's wit before hidden microphones—I have known all these situations, I have experienced them myself, yet none of them has given rise to the person my curriculum vitae and I represent. The characters in my novels are my own unrealized possibilities. That is why I am equally fond of them all and equally horrified by them. Each one has crossed a border that I myself have circumvented. It is that crossed border (the border beyond which my own "I" ends) which attracts me most. For beyond that border begins the secret the novel asks about. The novel is not the author's confession; it is an investigation of human life in the trap the world has become. (5.15.7)
Now we can start thinking about what the narrator (or author) is trying to do with his novel. Interestingly, he accomplishes with his novel everything that, according to his novel, we can't do in real life. He disrupts the linearity of time by telling a non-chronological narrative. He achieves a mini-version of eternal return by repeating the same scenes a second or third time. He claims in the passage above that his characters are "his own unrealized possibilities," which means he's using the novel as a way of giving weight to and taking responsibility for his decisions – he gets to compare his own life with different possible outcomes (as represented by his characters). The novel explores the human struggle to give our lives weight despite its necessary and unbearable lightness. And the novel itself is the narrator's attempt at doing just that for himself.