Peter's is the possessive form of the name Peter, showing that something belongs to him. In speech, it can also contract Peter is or Peter has, as in Peter's late or Peter's finished. Context decides which meaning fits.
The hand that rounded Peter's dome, And groined the aisles of Christian Rome, Wrought in a sad sincerity Himself from God he could not free He builded better than he knew The conscious stone to beauty grew. Ralph Waldo Emerson
If ordinary means I have suddenly got to produce a household of kids and iron Peter's shirts, I'm sorry, I'm not interested. Helen Clark
The pioneering instrument of reform was the Bank of England. Of all institutions concerned with economics none has for so long enjoyed such prestige. It is, in all respects, to money as St. Peter's is to Faith. John Kenneth Galbraith
Let the blessing of St. Peter's Master be...upon all that are lovers of virtue, and dare trust in his Providence, and be quiet and go a-angling. Izaak Walton
Ender didn't like fighting. He didn't like Peter's kind, the strong against the weak, and he didn't like his own kind either, the smart against the stupid. Orson Scott Card
A scene like Peter's denial fits into no antique genre. It is too serious for comedy, too contemporary and everyday for tragedy, politically too insignificant for history-and the form which was given it is one of such immediacy that its like does not exist in the literature of antiquity. Erich Auerbach