The Gathering of Israel - 3 Nephi 21: 1-7

1 AND verily I say unto you, I give unto you a sign, that ye may know the time when these things shall be about to take place—that I shall gather in, from their long dispersion, my people, O house of Israel, and shall establish again among them my Zion;
2 And behold, this is the thing which I will give unto you for a sign—for verily I say unto you that when these things which I declare unto you, and which I shall declare unto you hereafter of myself, and by the power of the Holy Ghost which shall be given unto you of the Father, shall be made known unto the Gentiles that they may know concerning this people who are a remnant of the house of Jacob, and concerning this my people who shall be scattered by them;
3 Verily, verily, I say unto you, when these things shall be made known unto them of the Father, and shall come forth of the Father, from them unto you;
4 For it is wisdom in the Father that they should be established in this land, and be set up as a free people by the power of the Father, 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;
5 Therefore, when these works and the works which shall be wrought among you hereafter shall come forth from the Gentiles, unto your seed which shall dwindle in unbelief because of iniquity;
6 For thus it behooveth the Father that it should come forth from the Gentiles, that he may show forth his power unto the Gentiles, for this cause that the Gentiles, if they will not harden their hearts, that they may repent and come unto me and be baptized in my name and know of the true points of my doctrine, that they may be numbered among my people, O house of Israel;
7 And when these things come to pass that thy seed shall begin to know these things—it shall be a sign unto them, that they may know that the work of the Father hath already commenced unto the fulfilling of the covenant which he hath made unto the people who are of the house of Israel.

(Book of Mormon | 3 Nephi 21:1 - 7)

The Lord will provide a sign as to when He is about to gather in the House of Israel from its long dispersion.

The words of the Lord to the people on the American Continent will be made known to the Gentiles, via the Book of Mormon. The Gentiles will believe the words of the Lord, and will publish them and bring them to the remnant of the seed of Lehi. They will receive the words of their ancestors from the Gentiles so that Gentiles may also lay claim to the blessings of salvation that come from the Savior.

The Gentiles will live as a free people on this land; free from the tyranny of despots and unrighteous kings. They will be free to believe as they see fit.
This gift, the ability to worship as I choose seems to be a rare thing throughout the history of the earth. Even today it is rare. China recognizes no religion, because they want their people to believe in the power of the state. There are other places where the belief system is dictated to the people. They can choose to believe what those in authority tell them to believe, or be persecuted and sometimes killed.

In my own country, religious intolerance rears its ugly head from time to time. Currently in the state of Texas, the government has abducted 416 children. Do I personally agree with the teachings of the FLDS? No. To paraphrase Jacob 2, their practices are an abomination before the Lord. However, to snatch an entire community of children from their parents based on an unsubstantiated phone call and a follicle of hair in a bed, seems rather heavy handed, and begs the question, if the state can do it to them, then why not to me, or to you, whatever your belief system is. But I digress.

The Lord will bring his words to the House of Israel via the Gentiles. If the Gentiles accept the words of the Lord they will be numbered with the House of Israel, hence we see that salvation is available to all that will accept it.
As the Book of Mormon and its teachings cover the face of the earth, the Lord is fulfilling the covenant that he made to Abraham.