It occurs 9 times in the Book of Mormon--twice in the introductory pages and 7 other times, all contained within 2 short spans: 1 Nephi 10-15 and 3 Nephi 16-20.
Interestingly, the majority of these references seem to be referring to the latter-day restoration of the gospel ("the dispensation of the fulness of times"). The gathering and covenants are also mentioned prominently.
1 Nephi 10
14 And after the house of should be scattered they should be together again; or, in fine, after the had received the fulness of the , the natural branches of the , or the of the house of , should be grafted in, or to the knowledge of the true Messiah, their Lord and their Redeemer.
1 Nephi 13
24 And the angel of the Lord said unto me: Thou hast beheld that the proceeded forth from the mouth of a Jew; and when it proceeded forth from the mouth of a Jew it contained the fulness of the gospel of the Lord, of whom the twelve apostles bear record; and they bear record according to the truth which is in the Lamb of God.
1 Nephi 15
13 And now, the thing which our father meaneth concerning the grafting in of the natural branches through the fulness of the Gentiles, is, that in the latter days, when our seed shall have in unbelief, yea, for the space of many years, and many generations after the shall be manifested in body unto the children of men, then shall the fulness of the of the Messiah come unto the Gentiles, and from the unto the remnant of our seed—
14 And at that day shall the remnant of our that they are of the house of Israel, and that they are the people of the Lord; and then shall they know and to the of their forefathers, and also to the knowledge of the gospel of their Redeemer, which was ministered unto their fathers by him; wherefore, they shall come to the knowledge of their Redeemer and the very points of his doctrine, that they may know how to come unto him and be saved.
3 Nephi 16
5 And then will I them in from the four quarters of the earth; and then will I fulfil the which the Father hath made unto all the people of the .6 And blessed are the , because of their belief in me, in and of the Holy Ghost, which unto them of me and of the Father.
7 Behold, because of their belief in me, saith the Father, and because of the unbelief of you, O house of Israel, in the shall the truth come unto the , that the fulness of these things shall be made known unto them.
...10 And thus commandeth the Father that I should say unto you: At that day when the Gentiles shall against my gospel, and shall reject the fulness of my gospel, and shall be in the pride of their hearts above all nations, and above all the people of the whole earth, and shall be filled with all manner of lyings, and of deceits, and of mischiefs, and all manner of hypocrisy, and , and , and whoredoms, and of secret abominations; and if they shall do all those things, and shall the fulness of my gospel, behold, saith the Father, I will bring the fulness of my gospel from among them.
11 And then will I my covenant which I have made unto my people, O house of Israel, and I will bring my gospel unto them.
12 And I will show unto thee, O house of Israel, that the Gentiles shall not have power over you; but I will remember my covenant unto you, O house of Israel, and ye shall come unto the of the fulness of my gospel.
3 Nephi 20
28 And they shall be a unto the people of this land. Nevertheless, when they shall have received the fulness of my gospel, then if they shall harden their hearts against me I will return their upon their own heads, saith the Father.
29 And I will the covenant which I have made with my people; and I have covenanted with them that I would them together in mine own due time, that I would give unto them again the of their fathers for their inheritance, which is the land of Jerusalem, which is the promised land unto them forever, saith the Father.30 And it shall come to pass that the time cometh, when the fulness of my gospel shall be preached unto them;
31 And they shall in me, that I am Jesus Christ, the Son of God, and shall pray unto the Father in my name.
32 Then shall their lift up their voice, and with the voice together shall they sing; for they shall see eye to eye.
Testimony of the Prophet Joseph Smith:
“He called me by name, and said unto me that he was a messenger sent from the presence of God to me, and that his name was Moroni; that God had a work for me to do; and that my name should be had for good and evil among all nations, kindreds, and tongues, or that it should be both good and evil spoken of among all people.
“He said there was a book deposited, written upon gold plates, giving an account of the former inhabitants of this continent, and the source from whence they sprang. He also said that the fulness of the everlasting Gospel was contained in it, as delivered by the Savior to the ancient inhabitants;
What does all of this mean?
I see a few important takeaways from studying this phrase.
First, anyone who wants to argue that Joseph Smith invented the text of the Book of Mormon needs to account for this rich covenant/gathering/fulness of the gospel theme in the Book of Mormon text, which was set in type in 1829, although the temple endowment and other parts of the restoration were still a decade away at this time. Talk about a long con!
Second, I believe the importance of the temple covenants are perhaps greatly underappreciated in the Church. The fulness of the gospel of Jesus Christ has to do with making and keeping covenants in order to be cleansed by the "blood of the Lamb."
Early church apostle David W. Patten said this about the dispensation of the fulness of times in 1838:
“The dispensation of the fullness of times is made up of all the dispensations that ever have been given since the world began, until this time … in the which all things shall be fulfilled that have been spoken of since the earth was made. …
“Joseph Smith, the leader of this dispensation] must be clothed with the power of all other dispensations, or his dispensation could not be called dispensation of the fullness of times. …
“Therefore, brethren, beware concerning yourselves, that you sin not against the authority of this dispensation, nor think lightly of those whom God has counted worthy for so great a calling.” (In History of the Church, 3:51–53.)
When we accept the fulness of the gospel (by making and keeping covenants) God gathers us together. When we reject the fulness of the gospel, we are scattered. This dispensation was prophesied to be the time of the final gathering of the House of Israel.