The bow contest takes place in book 21 of The Odyssey. The purpose is that the winner will have Penelope's hand in marriage. She presents the contest by saying:
Come now, ye wooers since this is shown to be your prize. I will set before you the great bow of divine Odysseus, and whosoever shall most easily string the bow in his hands and shoot an arrow through all twelve axes, with him will I go, and forsake this house of my wedded life.
When Odysseus, disguised as an old beggar, says he will try to string the bow, the suitors all vehemently object. They are actually afraid that he will succeed and make them look bad. Eurymachus, one of the suitors, tells Penelope that he and the other suitors would not want people gossiping that an old beggar won her hand instead of a far more eligible suitor. Penelope responds by scolding the suitors for insulting the beggar, who is her guest.
When Odysseus takes up the bow and effortlessly strings it, the suitors' attitude changes to one of shock. They are stunned into silence that they were bested by a mere beggar. At that moment, Zeus sends a thunderclap to break the silence.