One of the first references to Zion in the Bible is:
Nevertheless David took the strong hold of Zion: the same is the city of David. (2 Samuel 5:7).
This scripture refers to a military battle in which David captured a fortress on Mount Zion from the Jebusites.
Mount Zion is a hill outside the walls of the Old City of Jerusalem. The name Zion also became a synonym for Jerusalem itself.
Zion is used 197 times in the King James Bible. This number includes the alternate spelling Sion.
An example which foreshadowed the exile of the Jews to Babylon is:
By the rivers of Babylon, there we sat down, yea, we wept, when we remembered Zion. (Psalm 137:1)
“Return to Zion” refers the return of the Jews from the Babylonian exile to the Land of Israel after the destruction of the First Temple, following the decree of Cyrus the Great. These events are recorded in the Bible books of Ezra and Nehemiah.
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Zion is also used to refer to Solomon’s Temple in Jerusalem.
In Salem also is his tabernacle, and his dwelling place in Zion. (Psalm 76:2)
The temple is understood to be God’s dwelling place.
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The phrase “daughter of Zion (or Sion)” is given 28 times in the Bible.
The apostle John wrote of Jesus triumphal entry into Jerusalem in the days before the Last Supper.
Fear not daughter of Sion, behold, thy King cometh, sitting on an ass’s colt. (John 12:15)
This was a fulfillment of Zechariah 9:9.
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Zion is used 45 times in the Book of Mormon, including references to Isaiah scriptures.
A few examples are:
1 Nephi 13
 And blessed are they who shall seek to bring forth my Zion at that day, for they shall have the gift and the power of the Holy Ghost; and if they endure unto the end they shall be lifted up at the last day, and shall be saved in the everlasting kingdom of the Lamb; and whoso shall publish peace, yea, tidings of great joy, how beautiful upon the mountains shall they be.
3 Nephi 21
 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;
 And awake, and arise from the dust, O Jerusalem; yea, and put on thy beautiful garments, O daughter of Zion; and strengthen thy stakes and enlarge thy borders forever, that thou mayest no more be confounded, that the covenants of the Eternal Father which he hath made unto thee, O house of Israel, may be fulfilled.
(Cross reference: Isaiah 52:7-8)
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Zion is also used several times in the Doctrine & Covenants.
An example is:
Therefore, verily, thus saith the Lord, let Zion rejoice, for this is Zion—the pure in heart; therefore, let Zion rejoice, while all the wicked shall mourn. (Doctrine & Covenants 97:21)
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“The building up of Zion is a cause that has interested the people of God in every age; it is a theme upon which prophets, priests and kings have dwelt with peculiar delight; they have looked forward with joyful anticipation to the day in which we live; and fired with heavenly and joyful anticipations they have sung and written and prophesied of this our day; but they died without the sight; we are the favored people that God has made choice of to bring about the Latter-day glory.”
– The Prophet Joseph Smith Jr.
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“Zion is both a place and a people. Zion was the name given to the ancient city of Enoch in the days before the Flood. ‘And it came to pass in his days, that he built a city that was called the City of Holiness, even Zion’ (Moses 7:19). This Zion endured for some 365 years (see Moses 7:68). The scriptural record states, ‘And Enoch and all his people walked with God, and he dwelt in the midst of Zion; and it came to pass that Zion was not, for God received it up into his own bosom; and from thence went forth the saying, Zion is fled’ (Moses 7:69). . . .
“The Lord called Enoch’s people Zion ‘because they were of one heart and one mind, and dwelt in righteousness; and there was no poor among them’ (Moses 7:18). Elsewhere He said, ‘For this is Zion—the pure in heart’ (D&C 97:21).”
Elder D. Todd Christofferson, “Come to Zion,” Ensign, Nov. 2008
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– Tom Irvine