Elder Mark E. Petersen has explained the significance of this verse as follows:
I take you back now to the time when the Savior was ministering in America. I hope that each one of you will read 3 Nephi 21. It is extremely significant. It is meaningful to us as Americans and as Latter-day Saints who live right now. You will recall that the Savior was talking to the Nephites about the Gentiles who would occupy this country in the latter days. He talked about the destiny of America, and explained why there would be a United States. Among other things, he said this:" . . . it is wisdom in the Father that they [the Gentiles in this country] should be established in this land, and be set up as a free people by the power of the Father. . . ."
Then he gives the reason. He had been talking about the gospel; he had been talking about the predictions; he had been talking about . . . the records which eventually became the Book of Mormon. He said that this great modern nation of the Gentiles should be established on this land as a free people. And now I quote directly:
". . . that these things might come forth from them unto a remnant of your seed, that the covenant of the Father may be fulfilled which he hath covenanted with his people, O house of Israel." (3 Nephi 21:4.)
That is the reason there is an America. That is the destiny of America. The Almighty kept this land free from other people until such time as he was ready to establish our nation. . . .
So, . . . this is God's land. He raised it up specially as he has raised up no other nation. He has given us our flag. So far as I am concerned the flag of the United States is the flag of Almighty God.
Old Glory to me stands for everything that the gospel of Christ stands for, because Old Glory was raised up because there was to be a restoration of the gospel. I cannot separate my flag and my religion. I would fight for my flag as I would fight for my religion. (BYU Speeches of the Year, 1968.)