This incident occurs in Book 8 of the Odyssey. Crucially, we must remember that King Alcinous does not know the true identity of his "guest", Odysseus. Having offered his daughter's hand to his guest, Alcinous calls a meeting of his counsellors, where he proposes to let his guest have a ship so that he can return to his homeland. This suggestion is approved, and Alcinous declares that there will be a feast and games in honour of his guest.
During the feast, a blind bard called Demodocus sings of the quarrel between Odysseus and Achilles at the Battle of Troy. The dramatic irony here is that we know Odysseus' real identity, so it is ironic that everyone appreciates the skill of the Bard and greatly enjoys the music, whilst Odysseus weeps at the revival of painful memories. Alcinous, seeing the grief of his guest, starts the games.
Although Odysseus is invited to participate in the games, he refuses, overcome by his many hardships. This is until one of the young athletes, Broadsea, insults Odysseus and goads him into participation, where he easily wins.