The significant artifact Odysseus possessed in the Trojan War is the Trojan Horse. This ingenious creation allowed Greek soldiers to infiltrate the city of Troy, leading to its eventual downfall. The clever use of deception highlights Odysseus's intelligence and strategic prowess, demonstrating the importance of cunning over brute strength in warfare. This event is a pivotal moment in mythology, representing the themes of trickery, ingenuity, and the transformative nature of conflict in human history.