Mormon does not tell us any particular reason for the prosperity in the land, only that it happens, and as a result of the prosperity, many join the church. This connection is interesting, as prosperity in the Book of Mormon is linked to temporal prosperity, and the acquisition of temporal goods and ideas is also the classic impetus to the pride of place that violates the Nephite egalitarian ideal and begins to cause contention. In this case, however, we are probably at the early end of this problem, and the earliest manifestations are apparently not as complication by the importing of ideas along with the goods.
Reading between the lines, it appears that the cessation of the wars and contentions allowed the Nephites to work at their economic health, and they were able to prosper. We might guess that since the government of the people and the main religion of the people were tightly intertwined, that the people would have seen this prosperity as a manifestation of God’s favor upon the ruling government and religion, and it was this apparent favor of God that convinced people to join more closely to the church that was so intimately connected to the political government.