Odysseus is disguised as an old beggar. When he takes up the bow, some of the suitors laugh him to scorn. They ridicule the old beggar, not realizing it is Odysseus. The suitors are despicable. They have taken advantage of Penelope and Telemachus. They have eaten more than their share and have drunk so much wine. They have worn out their welcome. Most importantly, they are planning to kill Telemachus.
When Penelope creates the contest of agreeing to marry whoever can string the bow and shoot it through a series of small circles, the suitors make fun of the old beggar, knowing or thinking he is too old to string the bow.
When Odysseus does string the bow, he wins the contest. This is when he reveals himself to the suitors who realize they are about to die at the hand of the hero Odysseus. Odysseus is alive and well, and he takes back his kingdom.