People really remember Debbie Reynolds due to her iconic movie and theatrical roles. Her lead role in "Singin' in the Rain" brought her to great acclaim. She also performed on Broadway. She was nominated for an Academy Award, a Golden Globe, a Daytime Emmy, and a Tony Award. She also owned a dance studio and performed humanitarian work.
People remember Debbie Reynolds. Although she starred in movies decades ago, these were timeless classics, such as Singing in the Rain. She was also involved in a bitter divorce that was run in the tabloids. The outpouring of reaction to her death this week is clear evidence that people remember her.
People remember Debbie Reynolds for many things. There are even photos of Carrie Fisher watching her mother perform when she was a little girl. Debbie Fisher even lived next door to her daughter for a while. Fisher is known for many famous works as well as for being a Hollywood beauty.
After somebody dies, it's natural for us to make them "bigger" than they actually were so that we can talk about what we really want to talk about - ourselves. "This person was so important to ME because....." or "I'll always remember that time I was doing this listening to this song" are common themes around the internet after a celebrity passes. Because people just want to talk about the latest thing has affected them personally. It's natural.