Narrative analysis: Nephi has just finished the major narrative story of his life, and has shifted from condensing material from the Book of Lehi into writing his own story. At this point in the narration, Nephi clarifies his intention for the remainder of his work. He indicates that he is no longer interested in the story of his father (at least in that it will not be written on the current set of plates) and that he does not feel it important to reproduce the genealogy which is available on the brass plates.
Nephi never intended to make a complete copy of Lehi's record (1 Nephi 1:16 "And now I, Nephi, do not make a full account of the things which my father hath written, for he hath written many things which he saw in visions and in dreams; and he also hath written many things which he prophesied and spake unto his children, of which I shall not make a full account.") but at this point he is even more clear that very large portions of a possible record are being left out. Chapter 6 provides an introduction to Nephi's future readers which explains these "deletions" from Nephi's record.
Historical information: At this point in the text we receive the first indication that the small plates are a somewhat limited medium. Nephi declares that he is intentionally leaving out important information which could be found elsewhere specifically because he desire(s) the room. The plates had to be a difficult medium to write on. The production of the plates would have been fairly difficult, not to mention the requirement of finding the metal to forge into plates. While the plates do not physically run out of room until our text covers Omni, Nephi is already aware of the limitations at the earliest parts of his story.