If I were asked to define "supernatural", I would do so as follows.
In nature (or creation if you prefer), there is much that can be
described without reference to God. If I wish to describe the motion
of a canon ball's flight through the air, I do so using Newton's laws,
and not a mention of God in sight. This does not mean that I fail to
recognize God's hand in the canon ball's flight, indeed I do. But
this recognition does not play an active role in the description of
the cannon ball's motion. This would be an example of a natural
event. In contrast, let's take the example of Moses' parting of the
Red Sea. To describe and explain this event, one must directly invoke
the role of God. Acknowledging God's role is not just something I
choose to do, rather the event necessitates it. I cannot do justice
to the event without directly referring to the role of God. Even if
someday someone explained how in freak circumstances, the Red Sea
could become parted through normal physical laws, the fact that it
happened at that particular moment in history necessitates God's hand
for a full explanation. It is this necessity for the hand of God to
be included in the description, which distinguishes "supernatural"
events from "natural" ones.
Okay, that was my current best shot at a definition of "supernatural".
Feel free to rip it to shreds, or improve upon it and so on.
The argument against Christians using the notion of "supernatural"
that I have heard, is that supernatural is not a biblical concept.
The argument says that because the bible doesn't distinguish between
natural and supernatural, neither should we. Now I don't feel
comfortable with this. I feel that logically there really is a
difference between the natual and supernatural. Yet I'm not sure what
to make of this argument about supernatural not being biblical. Any
"They told me I was gullible ... and I believed them!"