The tale of the Trojan Horse plays a crucial role in the story of the Iliad by illustrating the themes of deception and strategy. After a prolonged siege, the Greeks built a massive wooden horse to secretly house their warriors, presenting it as a gift to the Trojans. This cunning ploy resulted in the downfall of Troy, reflecting how cleverness and trickery can triumph over brute force. The story underscores the significance of intellect over physical strength in warfare.