What makes prayer effective?

In a conversation a couple of years ago, a family member described all the symptoms of panic attacks she was having and said she was taking medication to control them. As she talked, I realized that I had been healed of these same symptoms over thirty years ago. I had completely forgotten about them. At the time, those symptoms had been aggressive to the point where I sometimes had to leave work early. 

Over the course of several months, I called a Christian Science practitioner many times for treatment through prayer. She stressed the truth in this Bible verse: “God hath not given us the spirit of fear; but of power, and of love, and of a sound mind” (II Timothy 1:7). She also often reminded me that I was relying on a Science that could be proved—that it is fact, not theory. The attacks became less frequent, and eventually just faded away and were forgotten. 

How was this accomplished? What is it that makes such prayer effective?