This perhaps has reference to the Nephite Church’s equivalent of our modern-day membership record system. Keeping a record of the members of the Church was not done for the sake of reporting statistics or “boasting” in numbers but rather so that each member could be identified and remembered.
The purpose is the same today. Members are remembered in that priesthood leaders are kept aware of all those in their units in order that, through priesthood quorums and auxiliaries and through effective home teaching, the Saints can be spiritually ministered to and encouraged to live the gospel to be mindful of the need for prayer, and to more faithfully rely upon the merciful arm of the Savior.
We do not know exactly what procedures and/or programs were employed by the Nephite Church to meet these objectives, but we can clearly see that the responsibilities of fellowshipping and nurturing one another, of being our “brother’s keeper,” is an age-old requirement of all of the Lord’s Saints. (Compare D&C 20:42, 46-55).