While this verse appears to be a recitation of the story of the Exodus, it is a very pointed attack at Laman and Lemuel. Nephi has previously noted their families hard time in the wilderness, and the miraculous assistance of the Lord. Having set the comparison between the Exodus and Lehi's family's travels, this verse is designed to hit at the hearts of Laman and Lemuel in a way that they cannot deny, and must see the correlation.
No longer content with an oblique reference, Nephi makes the correlation explicit: "And he did straiten them in the wilderness with his rod; for they hardened their hearts, even as ye have." Nephi reminds his brothers that the children of Israel in the desert suffered afflictions. Here Nephi boldly suggests that some of the afflictions might actually be the fault of Laman and Lemuel because of the hardness of their hearts. That suggestion must have hit them hard, as they have been blaming their troubles on Lehi, and now on Nephi, and yet now they hear that they might be the ones at fault.
As with other occasions when Nephi points out Laman and Lemuel's errors, he indicates that there is a way back. Nephi does not cut them off without hope, but uses the example of the children of Israel and the fiery flying serpents to show that there is a simple way back. He is obviously suggesting that Laman and Lemuel avail themselves of it.