Nephi sees that the future of his posterity lies in wars and rumors of wars. He sees that it will not always go well for his people, as in verse 2 he notes that there would be "great slaughters with the sword among my people". With so much prediction of violence, confirmed by later books in the Book of Mormon, it is remarkable that in the small plate record there is so little record of it. The reason lies in the charter of the small plates, and the division between them and the large plates of Nephi. The wars and rumors of wars are the stuff of the larger plates, with the small plates being reserved for a very different type of story.
It is also worth noting that there is no indication that these future events would be taking place on a different continent, in a new world. Whether or not that information was available to Nephi cannot be determined from this vision. Remember that the vision occurs in the travel away from Jerusalem, and perhaps not yet on a known path to a new distination.
Verse 3 contains an interesting juxtaposition of phrases. In the first phrase Nephi records that many generations pass. In the second clause he states "after the manner of wars and contentions in the land". The pairing of these phrases suggests that Nephi could tell the passage of generations due to the nature of wars among his people. What might this mean?
While not directly related to generations, it is possible that the wars are directly correlated to the passage of the years. John L. Sorenson examined the times for warfare in the Book of Mormon, and finds that wars were seasonal, and tended to be fought at a time when the agrarian soldiers were not needed in their fields (Sorenson, John L. "Seasons of War, Seasons of Peace in the Book of Mormon" Rediscovering the Book of Mormon. Provo:FARMS, 1991, 249-255.)
Of course the "after the manner of wars..." could also refer to the wars only, and indicate that they were typical, rather than attempting to tie them to a marking of the generations.