Peter was not a personal name in first-century Palestine. Someone, I think it was George Bernard Shaw, said, “The church was founded with a pun.” He was right. The intent of that remark may have been dismissive, but, as is usual with biblical puns, the wordplay of Jesus is far from trivial. In fact, the play on Simon's nickname is just one of several rich biblical allusions at work in this key passage.
Petros, the masculine form of the Greek word petra (“rock”—reflected in our English words “petrify” and “petroleum,” oil from rock rather than olives), translates the Aramaic kepha (“rock”). Kepha, or Peter, is a special name that Jesus gives Simon bar Jonah to signify his appointed mission.
Why Rock? We might call someone Rocky today to refer to his physical toughness. In Simon’s case the name more likely has biblical roots. First, there is the precedent of Isaiah 51:1-2, where the founding ancestors of the people of Israel, Abraham and Sarah, are called, respectively, “the rock from which you were hewn” and “the pit from which you were quarried.” Then there is the fact that the expected messiah was to be the builder of a new temple, just as in 2 Samuel 7 the son of David was to build a temple; and even though the first son of David, Solomon, built the first temple, the end-time Messiah was also expected to build the temple of the messianic age. When Jesus speaks of “building” his Church on the rock of Simon, he is of course speaking of a community, but the image is that of a physical structure, a temple. And temple does indeed become a favorite image of the early Church to describe itself (as in 1 Cor 3:10-16, 1 Pet 2:2-8, and Eph 2:19-22).
But, yes, the Church can be pictured as temple, but it is also a household. That image comes into play when Jesus speaks of giving Peter the keys to the kingdom. Isaiah 22, the First Reading this Sunday, provides the background. King Hezekiah's steward has abused his office and the prophet mediates the divine command that the king is to dismiss him and bestow the key of the house of David upon Eliakim. With the language of “keys to the kingdom,” Jesus appoints Peter as steward of the Church, now imaged as household—indeed, the spiritual household of the ultimate Son of David.
A further image comes into play when Jesus speaks of “binding and loosing” to describe Peter's authority. Binding and loosing refers to the authority of the chief rabbi of a community. Sometimes it referred to the application of the Torah to a particular case (the apparent reference here). Sometimes it referred to the power to include or exclude a member of the community (see Mt 18:18). Thus, Jesus makes Peter, in effect, chief rabbi of the community of the Church.
This passage has been a battleground of hostile debate between Protestants and Catholics. In some quarters it may still be that, but in today’s sober dialogue between Catholic and Lutheran scholars at least, a strong consensus has emerged that the Petrine ministry of overseeing the unity of the Church (historically realized by the Bishops of Rome) is an essential part of the New Testament’s presentation of the Church of Christ.
And so it is part of any Christian's discipleship to pray and work for the full realization of that ministry of unity, the reunion of a divided Church.