Jesus had commanded the people to update their scriptural records with new material when He was with them on the second day. On this occasion, he commands the twelve to write both of His visit, and of the works of the people.
The immediate reason given was that these things would be written in the Heavenly records, and from them the people would be judged.
There is another reason for this commandment, however. At that time, there was no Nephite nation. There were separate tribes about whom we know nothing after the great destructions that witnessed to Christ’s death in the Old World. Thus, there was the possibility that the tradition of keeping the plates of Nephi might have ended. Jesus commands that it continue. It was possible to continue because the records had been kept by Nephi (son of Nephi) and the current head of the twelve disciples. The command to write what Christ had said may have been taken up by more than one of the twelve, but it certainly was taken up by Nephi. It is his record of this event that Mormon used in 3 Nephi.