Nephi has claimed a new land. He declares that they follow the law of Moses, which declares that they are a people attempting to live Jehovah’s commandments. The promise of the land is that should they be faithful, they will prosper. Therefore, right after stating that they are, and at least are attempting to be faithful, they “did prosper exceedingly.”
Prosperity is defined by reaping in abundance and having flocks and herds. Notice how similar this is to Nephi’s statement of the benefit of the land after they landed:
"And it came to pass that after we had sailed for the space of many days we did arrive at the promised land; and we went forth upon the land, and did pitch our tents; and we did call it the promised land.
"And it came to pass that we did begin to till the earth, and we began to plant seeds; yea, we did put all our seeds into the earth, which we had brought from the land of Jerusalem. And it came to pass that they did grow exceedingly; wherefore, we were blessed in abundance.
"And it came to pass that we did find upon the land of promise, as we journeyed in the wilderness, that there were beasts in the forests of every kind, both the cow and the ox, and the ass and the horse, and the goat and the wild goat, and all manner of wild animals, which were for the use of men." (1 Nephi 18:23–25)
Nephi clearly sees the ability to provide for a people as the definition of prospering in the land. Both after their arrival in the New World and after their arrival in a new part of that land that the Nephites will claim as theirs, Nephi declares that they prospered and had abundance to eat. It is important for the nature of society that he mentions tilling first, and animal husbandry second. That is the relationship that stable communities have. Agriculture will be the basis for their increasing population, with animal husbandry an important, but perhaps distant, supplement.