The story of the tortoise and the hare teaches several lessons about teamwork and competition. Initially, the hare loses by being overconfident and resting, but wins the rematch by running consistently. Next, the tortoise wins by changing the rules to favor its strength of swimming. Finally, they realize teamwork is best and cross the finish line together by helping each other's strengths. The key lessons are to work to your competencies, compete against situations rather than rivals, and that teams outperform individuals.