Question

In the story, my sister's keeper, who is the sister's keeper? Why?

Answer 1

The main character of the story name is Anna, she was born essentially to donate organ to her sick sister Katie. So in this regard she is her sister "keeper" because she is keeping her alive. When she goes to fight in court for her right to CHOOSE whether or not she is to give organs to her sister it is revealed that she never wanted to stop trying to save her sister, (so she is still wishing to be her sisters keeper) but just doesn't want to be forced to do it. 
Hope this helps :) 

Answer 2

In this story, "My sister's keeper", the main character Anna, is the keeper because she must donate organs and blood to her sister to keep her alive.