The speaker had a realization about success when it was revealed that a person they admired was doping, leading to a shift in their perspective. They realized that true success is not measured by material accomplishments, but by one's character and who they are. The speaker highlighted the importance of having a 'to be' list along with a 'to do' list, focusing on traits like generosity, wisdom, and compassion to cultivate a becoming mindset rather than just an accomplishing mindset.