The gathering of Israel is a very common Old Testament and Book of Mormon theme. Joseph Smith stated, we believe in the literal gathering of Israel and in the restoration of the Ten Tribes (A of F 10). The gathering of Israel must be understood in two contexts, the literal gathering and the spiritual gathering.
The first, or literal gathering, refers to the reestablishment of state of Israel with the literal immigration of thousands of Jews from all over the world to the new sovereign. This has been going on for decades and continues at an accelerated rate. The literal gathering is also fulfilled in the immigration of Gentiles adopted into the house of Israel by accepting the gospel of Jesus Christ, accepting baptism, and them moving to a main body of saints. This was the practice in the early days of the church and will likely be reinstituted in a gathering to Zion (the New Jerusalem) prior to the Second Coming. The third component of the literal gathering will occur when the ten tribes return to Zion to receive their temple blessings at the hands of the children of Ephraim (DC 133:26-32).
The spiritual gathering of Israel represents the unity of spirit and purpose of all those who are brought into the fold of God. That these individuals do not have to be in the same geographic location is seen in the words of the Savior, other sheep I have, which are not of this fold: them also I must bring, and they shall hear my voice; and there shall be one fold, and one shepherd (Jn 10:16). In this scripture, the righteous Nephites/Lamanites are brought into one fold with the early Christian saints although they were separated by an ocean of water. Thus these two groups had been spiritually gathered into one fold. In the latter-days, the spiritual gathering is just the same. Any member of the house of Israel who believes in Jesus Christ and receives saving ordinances is brought into the common fold of the kingdom of God on earth. Most scriptures about the gathering of Israel are used in this context.