15 He saith unto them, But whom say ye that I am?
16 And Simon Peter answered and said, Thou art the Christ, the Son of the living God.
17 And Jesus answered and said unto him, Blessed art thou, Simon Bar-jona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven.
18 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.
19 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.
This scripture teaches several important points of doctrine. First of all, when the Savior asked Peter specifically, "..whom say ye that I am?", Peter answered that he was the Christ. Jesus then pointed out that this was not something that he learned from other people, but was personal revelation from Heavenly Father. This principle; revelation, is so important to the building up of the church, that the Savior said that it would be upon this rock, revelation, that the church would be built.
In addition to revelation, the Savior also taught Peter that he would give him the keys of the kingdom, or the Priesthood authority to guide the church. One aspect of this authority is that Peter then had the "sealing power", which includes the power to "seal" a husband and wife as an eternal couple.
As I was thinking about the "keys of the kingdom" today, I thought back to when my husband and I moved to China for 2 years. While we were gone, we enlisted a property manager to rent out our house. We gave him the keys of our house. We chose someone whom we felt we could trust, and someone whom we felt would do his job well. It was not his right to sell our house, or make any significant changes to it, but he could manage it for us. This is much like the authority given to Peter. He was given the authority to run the church, and also the revelation to know the Lord's will concerning what should be done. But it was not Peter's place to change the original structure or doctrine of the church, unless God so ordained.
Today we have a living prophet who also holds the "keys of the kingdom". He acts upon the principle of revelation to lead and guide the church. It is still Jesus Christ's church, and He stands at the head of it, but He gives the "keys"; the authority to the prophets to manage it. These keys also give them authority to carry out the different missions of the church. Some of the "keys" include the gathering of Israel, the mission of the redemption of the dead, and the sealing keys to bind families as eternal units. The same keys and revelation that Peter used to guide the church are again on the earth today.