The 1830 edition did not have the chapter break that separates our chapters 25 and 26 of 2 Nephi. The original chapter included our chapters 25, 26, and 27. Therefore, these verses were intended to follow immediately after Nephi’s discussion of the Messiah’s atoning mission.
After the atonement, the Messiah will rise from the dead. As part of his victory over death, he will appear to Nephi’s descendants. In 2 Nephi 25:12, Nephi had suggested that wars and rumors of wars would precede the coming of the Messiah. That theme is repeated here in the New World context. Nephi declares that many generations would pass, but then there would be great wars and contentions. Our understanding of Nephi history tells us that wars and contentions were frequently part of their challenges, but Nephi is using them as a sign of the coming of the Messiah.
It is after wars and contentions that the signs would be given of the Messiah’s birth. Indeed, there are wars and contentions that come before the New World appearance of the signs of the Messiah’s birth, and then death. During Nephi’s vision associated with the tree of life, he saw that future appearance of the Messiah, and saw that it came after tempests and great destructions. Those are the destructions that he is referencing here.