The following quotes are from:
David O. McKay, Ancient Apostles (Salt Lake City: Deseret Sunday School Union Board, 1969)
Simon is Called “Cephas”
And he brought him to Jesus, and when Jesus beheld him, he said, “thou art Simon the son of Jona: thou shalt be called Cephas, which is by interpretation, a stone” (or the Rock).
In those days the Jews spoke the Hebrew language; but the new Testament was written in the Greek language. Now, in Hebrew “Cephas” means “rock”; but in Greek the words for “rock” is “petras,” or “Peter.” So from that time, Simon was known as Simon Peter, or “Simon, the Rock. (p. 9)
Genuine Faith
When Jesus called Simon “Peter” or “The Rock,” he undoubtedly expressed in that name one characteristic which he desired to see in the faith of his disciples, and particularly in each of his apostles. He desired them to possess a faith that was unwavering,--a faith that would make them steadfast in the truth regardless of miracles or the acts of men—a faith that would trust the Lord at all times and under all circumstances, let those times and circumstances be what they may. (p. 21)
“I say unto thee,” continued Jesus, “that thou art Peter and upon this rock will I build my church; and the gates of hell shall not prevail against it.”
Christ’s Church Built Upon Revelation
By that he meant that as Simon’s name “Peter” means rock, so this testimony that comes by revelation shall be the rock upon which Christ’s Church shall be built. Because when one receives such divine assurance in his soul that the gospel is true, no views of men, nor waves of temptation nor “the power of hell” can deprive him of it. You remember when Jesus first met Simon, he said he should be called “the Rock.” Ever since then it would seem that Jesus has been waiting for the time when Peter’s testimony would be like his character—expressive and firm. That time has come; and Peter is now prepared to receive a greater responsibility.
Keys of the Kingdom
“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.”
One key was to open the door of the gospel to the Gentiles, but it took quite a while before Peter knew how to use it.
It is one thing to know that the gospel is true; it is quite another thing to comprehend its purpose and significance. (p. 27)