Based on the words "being filled" in your question, I assume you are currenly reading the novel and have not yet finished it. This answer will not take into account how far along you are. (Consider this when creating your own answer or presenting discussion points in class.)
The "gap" created in the novel by Oskar's very limited point of view is essentially of the information he leaves out in the broader context of the story and its surrounding characters. Oskar's story is primarily about his own relationship with his father, mother, and grandmother. Due to his young age, lack of knowledge, and eccentric personality, many details which would paint a more clear picture are left untold by Oskar.
Because of this, the narration (beginning in chapter 2) switches from Oskar's point of view to a series of letters. The authors of these letters are at first left unknown. It becomes clear as the novel continues that these letters are written by Oskar's grandmother (to Oskar) and his grandfather (to Oskar's father). They provide deeper context and family history to Oskar's present story. In many ways, these letters primarily reveal difficulty in life and love for Oskar's grandmother, which, by the end of the book, serves as a further connection point between herself and Oskar.