Joseph Smith

What was the object of gathering … the people of God in any age of the world?... The main object was to build unto the Lord a house whereby He could reveal unto His people the ordinances of His house and the glories of His kingdom, and teach the people the way of salvation…. 

It is for the same purpose that God gathers together His people in the last days, to build unto the Lord a house to prepare them for the ordinances and endowments, washings and anointings, etc.... 

God ordained that He would save the dead, and would do it by gathering His people together.... 

Why gather the people together in this place?... To receive the ordinances, the blessings, and glories that God has in store for His Saints. (History of The Church, 5:422-427)

Brigham Young (President)

The ordinance of sealing must be performed here man to man [father to son], and woman to man, and children to parents, etc., until the chain of generation is made perfect in the sealing ordinances back to Father Adam; hence, we have been commanded to gather ourselves together, to come out of Babylon, and sanctify ourselves, and build up the Zion of our God, by building cities and temples, redeeming countries from the solitude of nature, until the earth is sanctified and prepared for the residence of God and angels. (Journal of Discourses, 12:165)

Bruce R. McConkie (Quorum of the Twelve)

Two things are accomplished by the gathering of Israel: First, those who have thus chosen Christ as their Shepherd; those who have taken upon themselves his name in the waters of baptism; those who are seeking to enjoy his Spirit here and now and to be inheritors of eternal life hereafter—such people need to be gathered together to strengthen each other and to help one another perfect their lives. 

And second, those who are seeking the highest rewards in eternity need to be where they can receive the blessings of the house of the Lord, both for themselves and for their ancestors in Israel who died without a knowledge of the gospel, but who would have received it with all their heart had opportunity afforded. 

Manifestly in the early days of this dispensation, this meant gathering to the mountain of the Lord’s house in the tops of the mountains of North America. There alone were congregations strong enough for the Saints to strengthen each other. There alone were the temples of the Most High where the fulness of the ordinances of exaltation are performed.

However, in the providences of Him who knoweth all things, in the providences of Him who scattered Israel and who is now gathering that favored people again, the day has now come when the fold of Christ is reaching out to the ends of the earth.... 

We are living in a new day. The Church of Jesus Christ of Latter-day Saints is fast becoming a worldwide church. Congregations of Saints are now, or soon will be, strong enough to support and sustain their members no matter where they reside. Temples are being built wherever the need justifies. (Ensign, May 1977, 115–18)