The significance of the Labors of Theseus in Greek stories lies in their representation of personal growth, heroism, and the confrontation of chaos. These labors, which include defeating the Minotaur and capturing various beasts, symbolize the struggle between civilization and barbarism. Through these challenges, Theseus evolves from a young hero into a wise leader, showcasing themes of courage, intellect, and the importance of moral integrity in achieving greatness.