In the Bible, I know it says that we have the ability to do anything that Jesus himself done. Not sure where or exactly how it is worded. As well it also states through Jesus all things are made possible.
Jesus, although God, laid his mantle of God down when he came to the earth. Everything he did, he did through the Holy Spirit living in him. The same Holy Spirit that lives within each of us. He showed us how it should be done - so the question is "why can't we do what He did?". We can, because its not us doing it but God working through us, and He is not limited. All we need to do is have faith - the bible says faith of a mustard seed can move mountains. To translate that into modern terms, the smallest amount of faith known can move the biggest thing known. I was at a healing conference by Currie Blake, and he gave an explanation of faith which i think is accurate - he said faith is not neccesarily belief in God, but rather it is standing on Gods word and trusting that He is faithful and will do what He has promised. Also, faith isnt a "measurable" quantity, but rather a quality - standing on His word is having faith.
Anyway, back to the question - part of Jesus' death was that He defeated sickness and ailments (his body, in Communion - sins were taken away by his blood). So, just like you accept forgiveness, in the same way you can accept healing. So when your aunt stands on that fact that Jesus defeated infirmity, and claims that the finger is healed / will be healed in Jesus' name, the finger has no option to heal.
I hope that all made sense. I'm trying to summarise a lot into a short explanation - its something which i have only recently learnt, so im still grasping it myself...
Graham