This is a frequently asked question on Google. I’m providing an answer here.
Warning: This contains spoilers for the end of Tim Burton’s Edward Scissorhands.
At the end of Edward Scissorhands, it is revealed that the elderly woman telling the story is actually Kim. She has not seen Edward Scissorhands in many years, allowing him to always remember her when she was young.
We then see the ageless Edward Scissorhands carving sculptures of Kim out of ice. Even after all this time, he still fondly recalls their time together.