Although we see the idea that small things may bring to pass great things in other statements in the Book of Mormon, the issue for this statement is not the meaning but rather what the “small and simple” thing was. The reference has to be the brightness of the brass plates mentioned in the previous verse (verse 5). The brass plates are undeniably old. They have been in the New World for nearly five hundred years at this point, and we have no way of knowing how old the oldest of the plates were when Nephi retrieved them from Laban.
Thus, they could be expected to be dimmed by time, yet they were not. It was not a big thing, but something Alma considered “small and simple.” Nevertheless, the brightness served as a sign of their sacred value. Alma uses the brass plates as his object lesson that “the Lord God doth work by means to bring about his great and eternal purposes.” At times there might be great miracles, but most often God works more subtly. Perhaps in our lives there are times when His hand is so subtle that we don’t even notice His guidance until long after the fact.