Nothing too dramatic but something sentimental. This is based on the new way in which Jem and Scout see Atticus in To Kill a Mockingbird after the Tim Johnson incident. I want to describe the incident, then say what I learned from it about that person or how I now see them in a new light.
Do you have a friend with whom you only do certain things, such as hang around together at school, but not in your neighborhood, or vice versa? Sometimes there is another side to these people about which the friend of one dimension knows nothing. For instance, a person who is rather timid around you appears on stage somewhere. Think about something like this-- a situation in which you see the friend in an entirely new light, one in which you can appreciate, too.
I think it will be best if you answer this question with a personal example. From your description, it sounds like it would be difficult for you to re-tell a story that belongs to someone else, especially when it comes to describing what "you learned" from the incident. I imagine that you are probably looking for some other examples to help you think of something on your own.
Most of the incidents from my own life that caused me to see a family member or close friend in a new light were one of two extremes: tragedy and humor. Somehow, tragic situations, emergencies (or near-emergencies) or other unexpected hard times tends to bring out different sides of people. I saw my mother cry for the first time in my life when our family dog died. Before this incident, I'd never seen such a soft side of her and it forever changed my childhood (and now adult) impression of her.
Unexpectedly funny situations always brought out the less serious side of my father. One year in Spokane, WA there was a terrible ice storm that left most of the city without power for several days (some even weeks). After a day and a half my dad braved the roads to drive to his work (a manufacturing plant) and retrieved a generator. I thought it was so funny that the first thing he decided to power up was our TV. In a time of seeming emergency, it was funny that the TV was what was deemed most important. He claimed it was for my mother. This incident showed a softer and more playful side of my father.
Both of these incidents stick out to me as moments that I learned my parents were just humans, and not necessarily super-human and emotionless, which, as a kid, I think I often assumed of them.