"I would suggest that the 'supernatural' is whatever cannot be explained by the physical laws of nature as we understand them, whereas a 'miracle' is a meaningful event, regardless of whether it happens within the laws of nature or outside of them.
The essential aspect of a miracle is its significance.
Its naturalness or unnaturalness is only its mechanism, its external manifestation.
To illustrate this in broad theological strokes, we may say that if the Almighty is not concerned with the actual agency of a miracle, then it should not matter to us either.
What matters is not how something happens, but the meaning associated with what happens.
This definition entails a change of conception, since even something that happens naturally can still be meaningful.
One who has been cured of a serious illness, for example, or escapes from a dangerous situation, recites the blessing of haGomel in synagogue, in which he publicly thanks God for having saved him.
This does not mean that recovering from illness or walking away from an accident unscathed is necessarily miraculous in the supernatural sense of the word, but only that it is significant.
And it is its significance that makes it miraculous."
From an essay "The Miracle of Purim" by Rabbi Adin Steinsaltz