The importance of the priesthood according to the Church of Jesus Christ of Latter-day Saints1:
...priesthood is the power and authority that God gives to man to act in all things necessary for the salvation of God’s children.
The priesthood includes the authority to administer ordinances of salvation to all human beings who are willing and worthy to accept them. Without the priesthood and the saving ordinances thereof, “the whole earth would be utterly wasted” (see Doctrine and Covenants 2:1–3; see also Doctrine and Covenants 84:21–22).
So the significance is that the authority to act with God's power was lost and none of the churches had that authority. With the restoration through Joseph Smith that authority and power is back on the earth.
Moroni did not restore the priesthood authority. Quick summary of the Priesthood leaving the earth, from Gospel Topics: Restoration of the Priesthood
When Jesus Christ was on the earth, He established His Church and gave His Apostles the priesthood, which is the power to act in His name (see Luke 9:1–2). After His Crucifixion and the death of His Apostles, priesthood authority and the fulness of the gospel were taken from the earth because of wickedness and a rejection of the truth (see 2 Thessalonians 2:1–3).
It continues on who restored the priesthood authority:
In the early 1800s, Heavenly Father and Jesus Christ restored the gospel to the earth through the Prophet Joseph Smith. This Restoration included the restoration of priesthood power and authority.
While Joseph Smith and Oliver Cowdery were working on the translation of the Book of Mormon, they read about baptism for the remission of sins. On May 15, 1829, they went to a wooded area near Joseph’s home in Harmony, Pennsylvania, and prayed about what they had learned.
In answer to their prayer, John the Baptist, under the direction of the Lord Jesus Christ, appeared and conferred upon them the Aaronic Priesthood, saying, “Upon you my fellow servants, in the name of Messiah I confer the Priesthood of Aaron, which holds the keys of the ministering of angels, and of the gospel of repentance, and of baptism by immersion for the remission of sins” (Doctrine and Covenants 13:1) ...
Sometime after John the Baptist’s appearance, the ancient Apostles Peter, James, and John also appeared to Joseph and Oliver, again under the direction of Jesus Christ, and conferred upon them the Melchizedek Priesthood (see Doctrine and Covenants 128:20). “The Melchizedek Priesthood holds the right of presidency, and has power and authority over all the offices in the church in all ages of the world, to administer in spiritual things” (Doctrine and Covenants 107:8). With this authority again on the earth, the Church of Jesus Christ could be restored in its fulness.
Where does Moroni fall in all of this? He is more tied to the Book of Mormon, than priesthood restoration (though it was during the translation of the Book of Mormon which led to the restoration of the Aaronic priesthood).
From Guide to the Scriptures, Moroni, Son of Mormon
Moroni sealed up the plates and hid them in the hill Cumorah (Morm. 8:14; Moro. 10:2). In 1823 Moroni was sent as a resurrected being to reveal the Book of Mormon to Joseph Smith (D&C 27:5; JS—H 1:30–42, 45). He instructed the young prophet each year from 1823 to 1827 (JS—H 1:54) and finally delivered the plates to him in 1827 (JS—H 1:59).
1 Gospel Topics: Priesthood