A religious ordinance is a practice that demonstrates the participant’s outward expression of faith. In Mormonism (the doctrine taught by The Church of Jesus Christ of Latter-day Saints), an ordinance is a sacred, formal act of special significance, often involving the making of covenants with God. Ordinances are performed by the authority of the priesthood and in the name of Jesus Christ.
What Latter-day Saints Believe
Two years before he was martyred in the jail in Carthage, Illinois, Joseph Smith, the first prophet and president of The Church of Jesus Christ of Latter-day Saints, wrote a letter to an editor by the name of John Wentworth in response to his request for information about the Church.
At the request of Mr. John Wentworth, Editor and Proprietor of the Chicago Democrat, I have written the following sketch of the rise, progress, persecution, and faith of the Latter-day Saints, of which I have the honor, under God, of being the founder. Mr. Wentworth says that he wishes to furnish Mr. [George] Barstow, a friend of his, who is writing the history of New Hampshire, with this document. As Mr. Barstow has taken the proper steps to obtain correct information, all that I shall ask at his hands, is, that he publish the account entire, ungarnished, and without misrepresentation. [History of the Church, 4:535–36; from a letter from Joseph Smith written at the request of John Wentworth and George Barstow, Nauvoo, Illinois, published in Times and Seasons, Mar. 1, 1842, p. 706. Mr. Barstow’s last name is incorrectly spelled “Bastow” in History of the Church and Times and Seasons.] 
At the conclusion of that letter, Joseph Smith outlined 13 essential points of belief that serve as a guide to direct Latter-day Saints in the basic principles of the gospel of Jesus Christ. Those 13 points became known as the Articles of Faith. The third, fourth, and fifth Articles of Faith of The Church of Jesus Christ clearly define the doctrinal teachings concerning the significance and value of ordinances.
3 We believe that through the Atonement of Christ, all mankind may be saved, by obedience to the laws and ordinances of the Gospel.
4 We believe that the first principles and ordinances of the Gospel are: first, Faith in the Lord Jesus Christ; second, Repentance; third, Baptism by immersion for the remission of sins; fourth, Laying on of hands for the gift of the Holy Ghost.
5 We believe that a man must be called of God, by prophecy, and by the laying on of hands by those who are in authority, to preach the Gospel and administer in the ordinances thereof.
Types of Ordinances
Several ordinances, such as baptism, confirmation, and sacrament (Eucharist, Passover or the Lord’s Supper) which are practiced by Latter-day Saints (inadvertently referred to as Mormons), are also practiced by other Christian denominations.
There are some ordinances such as baptism, confirmation, ordination to the Melchizedek Priesthood (for men), the temple endowment, and marriage sealings, which are essential to a person’s salvation and exaltation. These ordinances are referred to as the saving ordinances. With each of the saving ordinances, faithful Latter-day Saints enter into solemn covenants with the Lord. Some ordinances that are unique to Mormonism, such as the endowment and sealings, are performed only in temples of The Church of Jesus Christ.
Under the authority of the Priesthood, ordinances such as naming and blessing children, consecrating oil, administering to the sick and the afflicted, patriarchal blessings, and priesthood blessings (including father’s blessing) are also performed. These types of ordinances are known as non-saving ordinances, as they are not essential for obtaining salvation and exaltation. They do, however, provide comfort, guidance, and encouragement.
Mormonism further teaches that because of the importance and necessity of ordinances to a person’s salvation, even those who have passed on without receiving the saving ordinances (albeit through no fault of their own) cannot dwell in the presence of God unless they first accept the ordinances that are performed vicariously on their behalf by worthy Latter-day Saints in temples of The Church of Jesus Christ throughout the world.
Priesthood Authority, Ordinances, and Covenants
Henry B. Eyring, the First Counselor in the First Presidency of The Church of Jesus Christ of Latter-day Saints, in his address given during the 178th Annual General Conference of the Church titled The True and Living Church, perhaps summed up this subject best with his remarks. He stated,
This is the true Church, the only true Church, because in it are the keys of the priesthood. Only in this Church has the Lord lodged the power to seal on earth and to seal in heaven as He did in the time of the Apostle Peter. Those keys were restored to Joseph Smith, who then was authorized to confer them upon the members of the Quorum of the Twelve.
We have seen today a demonstration that this is the true and living Church. The keys of the priesthood are held by mortals, but the way has been prepared by the Lord for the keys to remain functioning on the earth so long as the people exercise faith both that the keys are on the earth and that they have been passed on by the will of God to His chosen servants.
Additionally, it is through the Church and the ordinances which are in it that the blessings of the sealing power reach into the spirit world. This is a true and living Church, reaching even to those who are no longer living. As you have the faith to find the names of your ancestors, as you go to the house of the Lord to offer them vicarious ordinances, you sustain this great work, whose purpose is to offer salvation to all of Heavenly Father’s children who come into this world.
Ordinances and covenants help us remember who we are. They remind us of our duty to God. The Lord has provided them to help us come unto Him and receive eternal life. When we honor them, He strengthens us spiritually.