The Savior is pulling citations from the scriptures not only to bolster his points, but to make his points. His last citation was from Micah 5, and this verse comes from Micah 4. The Lord takes Micah 4:12 and makes it his own by indicating that he will do the gathering. Thus there is an endtime promise first of the dominance of the House of Israel which rises after the gospel is given to the Gentiles, and then there is a gathering.
Cultural: The reference in Micah is to a horticultural image that would be well known in the Old World, but not in the New World. Nevertheless, this would be the text that was on the brass plates. There would probably have been some historical memory of the meaning of the concept since it was part of the brass plates, and certainly part of the cultural heritage of the Old World that could be passed down to interpret that verse.
Reference: The phrase “gathereth his sheaves into the floor” is found in Micah:
Micah 4:12
12 But they know not the thoughts of the LORD, neither understand they his counsel: for he shall gather them as the sheaves into the floor.