As a result of the dispersion of Israel, when Babylon carried away the Israelites, around 600 BC, many gospel truths were lost. Due to the House of Israel going its separate ways, differences of belief resulted. That is why we have so many different faiths. (Of course, some of these different faiths, as well as the House of Israel, started before 600 BC; and these other faiths also were started by people going their separate ways.)
In the scriptures, the opposite of the dispersal of Israel is the gathering of Israel, which is going on right now, by the Church of Jesus Christ of Latter-day Saints. Many truths which were forgotten have been brought back, like, for example, the reality that Jesus exists. So, this gathering of Israel is the effort to share with others the truths that existed before the dispersal.
Besides being prophesied in 1 Nephi 10:14, the gathering of Israel was also prophesied in the Old and New Testaments:
“I will bring you out from the people, and gather you out of the countries wherein ye have been scattered; and I will be sanctified in you before th heathen. And ye shall know that I am the Lord” (Ezekiel 20:41-42)
“That in the dispensation of the fullness of times he might gather together in one all things in Christ, both which are in heaven, and which are on earth; even in him” (Ephesians 1:10)
There are many other scriptural verses which also express this principle, of which I am thankful I am aware, and in which I am able to take to participate.
This is what I previously wrote after reading 1 Nephi 10: Why I Believe In Jesus