I find Lewis's use of the word 'magic' fascinating, really. I remember (though I cannot seem to locate the actual reference) that he at times would apply it to the sacraments (the real presence of Christ in the Eucharist, for example), and I am sure that he also considered the Church itself - the
mystical body of all faithful people - to be magical in some sense.
I think it is right to say that he was not speaking of witchcraft or innate ability or sleight-of-hand, but of something much more intrinsic. My understanding of his particular usage is difficult for me to articulate. Let me try it like this:
There is something in the nature of God, and in the nature of Man relative to God, such that God acts upon and in us through means which are inaccessable to our understanding. Not that we cannot know what is happening, or even why it has to happen in that way. Rather, it is magical, because He (with His perfect grasp of His own nature and ours) is communicating something to us or causing something in us or whatnot by means of a process we would never have guessed and cannot fully grasp. A process which is, nevertheless, inseparable from the very core of reality.
(A small clarification: He's not manipulating the forces of nature - physical or spiritual - and bending them to His will as a wizard or sorceror. He is instead working within the confines of the reality He has dictated to cause a thing. But I do not think this is a portion of reality that science can describe - I think it is part of that heavier portion of reality that is spiritual)
I'll use the example of the Eucharist again (a/n - I believe that Communion is more than a symbol. I don't think you have to believe this to agree with the point, but know that I am assuming it here). During Communion, God communicates some real thing through what appears to be just a sign - the elements of bread and wine. Through these elements, we are made to dwell in Christ and He in us - part of that indestructable Life which is in Him preserves us unto everlasting life. This is arguably not the entirety of the grace imparted, but I'm confining my point to it.
This giving of grace is, I think, part of the way Lewis uses 'magic.' The magic of it is that mysterious factor which only He can effect. Our participation in this (if any) must be dependant upon our knowledge about Him, because it is bound to the reality of His nature.
I think this is how Lewis uses the idea of magic in Narnia. The better the Narnians know (and especially love) Aslan, the more they have knowledge of the deep and deeper magic. When they know Him, they see the way in which they ought to use the authority He has given them - thus the good magic seen in Narnia. All the wicked magic is forced, twisting things to the will of the user.
I know this is already absurdly long, but one more thing. Divine intervention has been mentioned in this thread. I think the definition I have proposed is strongly connected to this, but that it is not quite the same thing. I speak of Divine action, certainly, but Divine intervention has the connotation of an interference with the natural order of things. I'm not usually one for letting connotation dictate usage, but this is so confusing that I want to be as clear as possible.
I'm afraid that this is very incoherent, but I'm not sure how to clarify it - please critique. Sorry about the length!