Some works of literature are known as confessionals. One of the most famous novels of this type is "Lolita" by Vladimir Nabokov. Nabokov's narrator, Humbert Humbert, uses retrospect to confess his obsession and sexual relationship with the young Delores Haze, among other things. Had Nabokov not used retrospect in this novel, it could not be considered a confession because the events of the novel would be happening to Humbert Humbert at the same time as he is relating them to us.
Sometimes an author will use the retrospective mode so he can look back on past events with clarity and an ability to make sense of what has happened. Memoirs rely almost exclusively on retrospect to communicate their stories, as the art form is based upon using wisdom to make meaning out of your past. For example, in his memoir "This Boy's Life," Tobias Wolff is able to look back on his childhood with the wisdom of his adult self, and tell a moving and wisdom-filled tale because of the choice.
Another reason to show that a narrator or character is looking back on past events is to show that the character has developed significantly since the beginning of the tale, and that the coming narrative will focus on how this transformation took place. This reason for retrospect is usually present every time the technique is used, which is often in conjunction with one or both of the reasons listed above.
One final reason an author might use a narrator that looks back on the events of the story is as a device to showcase a captivating narrative voice. When a narrator looks back on the past, he becomes the primary storyteller to the reader, and that storytelling voice becomes a specific lens through which the reader experiences the world of the story. Nabokov's Humbert Humbert is an example of this technique as well, as Humbert's voice is as much a factor in the success of the story as the narrative itself.