The promise made to Nephi is that the words of his people will be presented to his descendants. In this time period those words will come forth, and will be part of the process of the salvation of the Gentiles (part of the “marvelous work” that will bring them to repentance in verse 29:1) and part of the salvation of his branch of the house of Israel. Note that the promise is made not only to Nephi, but also to Lehi. By including Lehi as a source for the blessings on progeny, the Lord explicitly includes both the groups that will become known as Lamanite and Nephite in the Book of Mormon. The Book of Mormon will be for the restoration of both of those lineages.
Literary: The particular language used to describe the coming forth of the Book of Mormon is “my words shall hiss forth.” This is a reference to the language of Isaiah:
26 ¶ And he will lift up an ensign to the nations from far, and will hiss unto them from the end of the earth: and, behold, they shall come with speed swiftly:
Nephi uses the terminology not only to echo Isaianic language, but also to place the Book of Mormon in the same context as the passage in Isaiah. “Hiss” is used only here and in Isaiah 7 (in Isaiah’s writings) so it is not a common theme. In this particular context, the implied reference is Isaiah 5:26 for any who would understand the reference. Once referred to this passage, the Book of Mormon becomes symbolically equated with the ensign to the nations, matching the promise and context of Nephi’s passage.
This implicit reference to the ensign to the nations will occur again following 2 Nephi 30:9-15. Nephi cites Isaiah, and then leaves off precisely prior to the ensign to the nations passages. Contextually, his citations and reworkings of Isaiah point to the coming of the Book of Mormon as a part of the fulfillment of the ensign to the nations prophecy, but for some reason Nephi is content with the implication rather than making the connection concrete.