From Pope Benedict XVI's General Audience Catecheses on the Apostle Peter. Image is from a study guide on the talks by Amy Welborn, available as a free download here.
Peter's rash generosity does not protect him, however, from the risks connected with human weakness. Moreover, it is what we too can recognize in our own lives. Peter followed Jesus with enthusiasm, he overcame the trial of faith, abandoning himself to Christ. The moment comes, however, when he gives in to fear and falls: he betrays the Master (cf. Mk 14: 66-72).
The school of faith is not a triumphal march but a journey marked daily by suffering and love, trials and faithfulness. Peter, who promised absolute fidelity, knew the bitterness and humiliation of denial: the arrogant man learns the costly lesson of humility. Peter, too, must learn that he is weak and in need of forgiveness.
Once his attitude changes and he understands the truth of his weak heart of a believing sinner, he weeps in a fit of liberating repentance. After this weeping he is finally ready for his mission.