On God’s part, the oath and covenant of the priesthood means that those who obtain both the Aaronic and Melchizedek priesthoods and magnify their callings in the priesthood will obtain eternal life and receive all that the Father has. On His part this is an unchangeable and unbreakable oath. Section 2 President Smith reminds us that the whole gospel of Christ is just a series of covenants with rewards attached. When we receive the priesthood it is by covenant, and the reward for receiving that responsibility is everlasting life with God. As long as we keep our end of the covenant that will be our reward. The priesthood covenants affect both men and women equally, as do the blessings of the priesthood. Click on this link for further reading on women and the priesthood. The article also has a link to the original talk given by President Smith in the 1970 priesthood session of general conference. He reminds us that the priesthood does not derive its power from the offices of the priesthood, but the other way around. There is no office in the priesthood that is greater than the priesthood itself. All offices of the priesthood exist only to administer the covenants and needs of the priesthood. No one office in the priesthood is greater than any other office in the priesthood, even though a person will be called upon to lead others in the priesthood through certain offices. The office in the priesthood does not make the man, the it is the priesthood that makes the man. It is the priesthood, not the office that exalts us. It is personal worthiness, not the calling or office we hold that brings us exaltation in the end.... everything connected with this higher priesthood is designed and intended to prepare us to gain eternal life in the kingdom of God.In Conference Report, Oct. 1970, 90–91.
As the Lord’s agents we are bound by his law to do what he wants us to do regardless of personal feelings or worldly enticements.Men, of themselves, have no message of salvation or ability to save for eternity. Everything men do in the priesthood is with, and through delegated authority from God. Section 3 We are reminded that the oath is the most binding form of human speech known to man. So when the Father swears to us with an oath that if we keep our covenant we will receive certain blessings in return, we can put our faith and trust in that oath. The Lord has sworn that the oaths with which he has promised us exaltation are unchangeable and eternal. They are the same type of oaths he made about His Son, Jesus Christ when Christ was promised to be a high priest forever and to receive all that the Father has. All the Lord’s covenants are unchanging and are based on our faithfulness to the conditions of the covenant in question. Be we male or female, if we keep the covenants we will receive the blessings. All the covenants of this Church are designed to make us ready for the Celestial kingdom. There is no covenant in this Church for anything of a lower order. For lower orders no covenants are needed. Section 4 We all have the fullness of the priesthood, but those who are called upon to hold the offices of the priesthood are responsible for the administration and ministering of the blessings of the priesthood through their service and commitment to doing the will of the Lord. By that faithful discharge of their duties to represent the ministry of Christ in all things, they earn their exaltation. Each of us has but to fulfill our callings in the Church, perform service in the temples, and keep all the commandments to be assured that the blessings of eternity will be ours, all because of the covenants we have made with the Lord.
“Our Responsibilities as Priesthood Holders,” Ensign, June 1971, 49.