Some scholars calculate that this is the day when the Greek leader Odysseus returns home to Ithaca from the Trojan War. The story of Odysseus' trip from Troy back home to Ithaca in Greece is told in the ancient book Odyssey. It's a difficult trip that lasts ten years, with many trials and adventures.
When Odysseus finally reaches home, he's disguised as a beggar in order to see what's been going on in his absence. He finds several suitors trying to marry his wife, Penelope, as everyone assumes that he's long dead. Odysseus kills the suitors and reveals himself to Penelope.