A miracle is an event that is inexplicable by natural or scientific laws and accordingly gets attributed to some supernatural or praeternatural cause. Various religions often attribute a phenomenon characterized as miraculous to the actions of a supernatural being, (especially) a deity, a miracle worker, a saint, or a religious leader.
Informally, English-speakers often use the word miracle to characterise any beneficial event that is statistically unlikely but not contrary to the laws of nature, such as surviving a natural disaster, or simply a "wonderful" occurrence, regardless of likelihood (e.g. "the miracle of childbirth"). Some coincidences may be seen as miracles.
A true miracle would, by definition, be a non-natural phenomenon, leading many writers to dismiss miracles as physically impossible (that is, requiring violation of established laws of physics within their domain of validity) or impossible to confirm by their nature (because all possible physical mechanisms can never be ruled out). The former position is expressed (for instance) by Thomas Jefferson, and the latter by David Hume. Theologians typically say that, with divine providence, God regularly works through nature yet, as a creator, may work without, above, or against it as well.
A Japanese woman living in Spain miraculously emerges unscathed from an automobile accident. To show her gratitude she adopts a cat and names it Aristotle. Why is that?