Then he called his twelve disciples together, and gave them power and authority over all devils, and to cure diseases.
When Jesus Christ lived on the earth, he organized his church with twelve apostles and ordained them with the power of his priesthood. The priesthood allowed them to participate in his work.
As Christ neared the end of his ministry and life on the earth, he taught and prepared his apostles for the responsibility they would face in carrying out his work on the earth without him. The apostle Peter, along with the others, had the priesthood power to lead the church, perform ordinances, and bless lives just as Jesus Christ had done.
And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.
And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.
After Christ's death and the deaths of the apostles, the priesthood power was taken from the earth. Thousands of years later, these same apostles, along with John the Baptist, visited the prophet Joseph Smith and ordained him to the same priesthood that they had received at the hands of Jesus Christ. These keys and power have now been restored to the earth to bless the lives of men and women.
The messenger who visited us on this occasion and conferred this Priesthood upon us, said that his name was John, the same that is called John the Baptist in the New Testament, and that he acted under the direction of Peter, James, and John who held the keys of the Priesthood of Melchizedek, which Preisthood, he said, would in due time be conferred on us, and that I should be called the first Elder of the Church, and he (Oliver Cowdery) the second. It was on the fifteenth day of May, 1829, that we were ordained under the hand of this messenger, and baptized.
You can read even more about how Jesus Christ has restored his church and his priesthood to the earth right here.