Explain the organization of In the Time of the Butterflies in terms of narrative structure.What does Alvarez accomplish by organizing the novel...

Julia Alvarez begins the novel from the sole surviving sister's (Dede's) perspective.  Alvarez talks about herself as the "gringa Dominicana" coming to visit Dede to talk about the Mirabal sisters, so she puts herself, the author, out of the narrative structure as an outside "reporter", if you will.  This serves to distance the reader from the author, and make it much less "her" story of discovery of the history of the Mirabal sisters, and much more a story told by the sisters themselves.

Alvarez uses a pattern of switching between the sisters, narrating (fictionally, for three of them are dead and Dede's narrative was not written by her) each in the first person -- that is, from their own point of view.  The stories are like diary entries (and sometimes, such as in Mate's case, are written as journalling) and tell their own stories themselves.  Their narratives usually talk most about what happened to each of them respectively, but we learn much about events which happened to all of them (such as Papa's dead, in Mate's narrative) in these narratives.

Of course, the "I" narrative (first person) gives many advantages, emotionally, to the author.  Each first-person narrator can talk about their own thoughts and feelings, and put their own personal spin on events.  This draws the readers in and, in many cases, makes the reader sympathetic to the narrators.  It also makes it easy to contrast different people's reactions to the same events; each one of them, often, gets to comment on their own thoughts and actions individually.

Since this book was not set up to be true history (far too much of it is fictionalized to be even considered historical fiction, even though many real and true historical events are recounted in it) the switching first-person narrative structure makes each character of the sisters real and alive for the reader in a way that omniscient narrator (or non-fiction history) never could.  Alvarez wasn't attempting to write history; she was attempting to write a novel about real people, but from point of emotional meaning rather than historical.  This means the imaginative work of having each sister write the things that happened to her (something which did not occur in reality) can be used to create a work of art, rather than a work of history.  The truth of the work, then, is emotional or dramatic truth, rather than the truth of past events -- the history serves as the context rather than the end.