What did Death mean when he said, "she did not bacl away or try to fight me, but I knew that something told the girl I was there... she knew me and she looked me in my face and she did not look away.. we both moved on"?

This is a relatively straightforward statement. People face death in different ways; characters such as the "girl" recognize the moment when death arrives and is ready to face death. Death had other places to go as did the girl as she faced her own death.