A miracle is something that comes to us from beyond the world. It is an event that can't happen, but it does. It can't be explained scientifically.
Lewis gained attention beyond his academic circles through his unflinching affirmation of the supernatural - God, demons, miracles and all. How could a sophisticated Oxford professor believe in such fables in the 20th century? He took on the task to consider whether it was intellectually honest and realistic to automatically reject miracles.
He critiqued naturalism, which claims that miracles were impossible or at least so improbable that they can never be accepted. In his book Miracles, Lewis confronted naturalism - the belief that nature is all there is: a closed box of cause and effect. Super-naturalism sees nature as an open system, operated by natural law most of the time but open to intervention by God.
There are three negative ways to respond to miracles:
1. They are impossible. Unless we absolutely certain that there is no supernatural power (God) in the universe, we cannot dogmatically say that every claim of a miracle is false. Granted, miracles rare are but that does not mean that they are impossible. We can never assume that what we have experienced is all there is to reality. There is no argument to prove that miracles cannot happen.
2. They are improbable. Scottish philosopher, David Hume, allowed for no instance of a miracle because another explanation is always preferable. However, we cannot say that all reports of miracles are false, even if one of them did happen. You need to weigh the historical evidence for each unusual event before you exclude or accept it.
3. They are inappropriate. In Christianity, miracles have deceives significant, converging on Christ and demonstrating that he is the one sent by God. The miracles of Christ are not merely powerful acts for the sake of power - they show his compassion and demonstrate his identity.
We still serve a miracle-working God. Nothing is impossible with Him!
[Summarised from Chapter 8 of Art Lindsley's C.S. Lewis' Case for Christ]