As clear a definition of a miracle as I've encountered, and one that the various partisans of Science and Religion simply fail to grasp, either from sloppy thinking or from a perverse desire to see these old friends come to blows:

The concept of miracle which is permissible from the historical approach can be defined at its starting point as an abiding astonishment. The philosophizing and the religious person both wonder at the phenomenon, but the one neutralizes his wonder in ideal knowledge, while the other abides in that wonder; no knowledge, no cognition, can weaken his astonishment. Any causal explanation only deepens the wonder for him. The great turning-points in religious history are based on the fact that again and ever again an individual and a group attached to him wonder and keep on wondering; at a natural phenomenon, at a historical event, or at both together; always at something which intervenes fatefully in the life of this individual and this group. They sense and experience it as a wonder. This to be sure, is only the starting-point of the historical concept of wonder, but it cannot be explained away. Miracle is not something "supernatural" or "superhistorical", but an incident, an event which can be fully included in the objective, scientific nexus of nature and history; the vital meaning of which, however, for the person to whom it occurs, destroys the security of the whole nexus of knowledge for him, and explodes the fixity of the fields of experience named "Nature" and "History". Miracle is simply what happens; in so far as it meets people who are capable of receiving it, or prepared to receive it, as miracle. The extraordinary element favors this coming together, but it is not characteristic of it; the normal and ordinary can also undergo a transfiguration into miracle in the light of the suitable hour. -- Moses (1946)

In other words, miracles have to do with meaning and symbol, which is a higher level of organization than that of physical causes. To attempt to explain them as natural or supernatural is a reductionist fallacy, on the same order as trying explain biology only in terms of its chemistry (or, less frequently, in terms of some supraphysical 'vitalism'). As Konrad Lorenz argues, the rules of biology encompass the rules governing inanimate matter, without violating them but nonetheless introducing an element that is simply not present in the less organized structures. Life, in some senses, is a more restricted form of existence, but it is precisely these additional constraints that make possible its incredible diversity.

I am reminded of Tolstoy's observation of the paradox in military and political hierarchies, that it is the elements at the top, the generals and marshals, who are the most constrained.