The immediate result of loosing Nephi is that the Liahona works again, and Nephi’s prayer calms the storm. This becomes a direct indication that Nephi has now become the prophet, and therefore ruler and teacher, over not only his brethren, but over the whole family.
Ancient Israelites understood Jehovah as a god of storms, and when Nephi is able to invoke the calming of the storm, it is a clear signal that Jehovah is with him. When the Liahona works for him, it leads to his statement that “I, Nephi, did guide the ship.” He has become the leader.
The next verse is the beginning of the intended ending for 1 Nephi. It will not end where Nephi planned it, for reasons discussed later, but the arrival in the New World is the intended end. Thus, they arrive, and called it the promised land. Interestingly, they didn’t receive a revelation that it was a promised land, only that since they had arrived, it must have been.