What is significant about time switching back and fourth in The Brief Wondrous Life of Oscar Wao?

Diaz shifts not only back and forth in time, but also between different narrators, for a couple of different reasons.
First, the book itself focuses on Oscar, but it is also the story of his family. His mother, Beli, and his sister, Lola, are featured prominently throughout the novel. By going back and forth in time, Diaz introduces readers to these characters at different points in their lives and from different perspectives. Because his family plays such an important role in Oscar's life, it makes sense that Diaz wants us to know their backgrounds and motivations, and skipping around in time helps him to do this very effectively.
Second, just as the book is about Oscar's family, it is also about Dominican culture. There are multiple pressures on Oscar, and these pressures often arise as a result of his family's Dominican background. Although Oscar grew up in New Jersey, his family's Dominican culture is still very much an influence in his life, and we see this especially from his mother, Beli. By going back in time to her earlier years, we get a better understanding of what the Dominican Republic was like when she was growing up, what influenced her, and how all of those experiences have shaped her as a woman and a mother. This also allows Diaz to tell some of the history, political and otherwise, of the Dominican Republic and illustrate how that history has current effects on Dominicans, whether they currently live in the Dominican Republic, or elsewhere.
Ultimately, shifting between timeframes in any story is a fairly common rhetorical and strategic choice of many authors. These shifts allow them to tell deeper, more complex, and more layered stories that may span generations, just like we see in The Brief Wondrous Life of Oscar Wao.

Within works of fiction, flash backs (analepses) and flash forwards (or prolepses) are literary devices that an author uses to interrupt the current time in the novel and take the narrative backward or forward in time. Often, these inset stories within the larger narrative arc serve a bigger literary purpose. Introducing character and plot details at intentional moments within the larger story has bearing on how characters and themes develop.
 
In The Brief and Wondrous Life of Oscar Wao, Junot Diaz's narrative moves frequently not only from one time to another, but from one narrator to another as well. Like the Dominican culture around which the story revolves, the narrative texture is varied and colorful. In addition to mirroring the Dominican spirit, Diaz's narrative choices also serve a higher literary goal. Throughout Oscar Wao, Diaz describes the juxtaposing aspects of the Dominican-American experience. A few of the overarching themes include colonization vs. belonging, superstition vs. science, and masculinity vs. female power. 
 
By continually switching time periods throughout the novel, Diaz continues his examination of opposites, applying that same scrutiny on time: present vs. past. In my opinion, Diaz is using that juxtaposition to make the reader ask How different are these two things actually? Throughout the novel, we see parallels and similarities between each of Diaz's juxtaposed pairs, including present and past. Prolepsis and analepsis are just two devices Diaz uses to bring the reader's attention to the novel's central themes.