The aside gets extended because Nephi's brother Jacob has also seen the Savior. To this point, Nephi's train of thought moves from Isaiah's importance to his people to Isaiah's understanding of the Savior, which leads to Nephi's experience, which leads to Jacob's experience. Nephi then puts, for him, a definitive cap on his testimony of the Savior, as he indicates that there should be three witnesses.
Nephi is referring to the Deuteronomic law of witnesses:
Deut. 17:6 At the mouth of two witnesses, or three witnesses, shall he that is worthy of death be put to death; but at the mouth of one witness he shall not be put to death.
Deut. 19:15 One witness shall not rise up against a man for any iniquity, or for any sin, in any sin that he sinneth: at the mouth of two witnesses, or at the mouth of three witnesses, shall the matter be established.
This law of witnesses allows for the establishment of fact with a minimum of two, but probably a more certain reckoning with three witnesses. Nephi sees the three mentioned as this more firm witness establishing this Messiah to come. Nephi knows, however, that there shall be even more witnesses to come, and so states.