The oath and covenant of the priesthood in The Church of Jesus Christ of Latter-day Saints (LDS) is a sacred agreement between the individual receiving the priesthood and Heavenly Father. It involves two key parts:

1. The individual's covenant: Those who receive the priesthood promise to be faithful in magnifying their priesthood callings, to live by every word that proceeds from the mouth of God, and to obey all the commandments. This also includes living and serving as Jesus Christ did, and for those with the Melchizedek Priesthood, to marry for time and all eternity in the patriarchal order.
2. God's oath (promise) to the individual: If the individual is faithful and keeps their part of the covenant, God promises several blessings including sanctification by the Spirit unto the renewing of their bodies, becoming numbered with the elect of God, becoming the sons of Moses, Aaron, and the seed of Abraham, and ultimately inheriting all that the Father has. This includes exaltation and godhood, being joint-heirs with Christ, and having eternal increase.

In essence, the oath and covenant entail a solemn contract where the individual promises faithfulness and magnifying their priesthood responsibilities, and in return, God guarantees eternal blessings and exaltation. This covenant is described in detail in Doctrine and Covenants Section 84 and is considered one of the most sacred agreements in the gospel.